The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X X X X 1 X X X X 1 0 1 1 X 1 1 X X X 1 1 1
0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X X X X X X X 0 X X X X 0 X 0 0 0 X X X X 0 0 0 X X X X X 0 0 0 X 0 X 0 X 0 X X 0 0 0
0 0 X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 X X X X X X X 0 0 0 X 0 0 0 X X X 0 0 0 X X X X 0 0 0 X X 0 0 X 0 X 0 0 X X X X 0 X 0 0 0 0 0 0
0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 0 X X X X X X 0 0 0 0 X 0 X X X 0 X 0 0 X X 0 0 0 X X 0 X 0 X X X 0 X X X 0 0 0 X 0 X X 0 X 0 0 0 0 0
0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 X X X X X X 0 X X 0 X X X 0 0 0 X X X X X 0 X X 0 0 0 0 0 X X 0 0 X X 0 X 0 X 0 0 X 0 0 0 X 0 0 0 0 0 0
0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X 0 X X 0 X 0 X 0 X X X X 0 0 X X 0 0 0 X 0 X 0 0 0 X X 0 0 0 0 X 0 X 0 0 X X 0 X X X X X 0 X 0 0 0 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X X X X 0 X X 0 X 0 X 0 0 X 0 0 X X X 0 0 0 0 X 0 0 X X 0 X X 0 0 X 0 0 0 X X X 0 0 0 0 X 0 0 0 X X 0
0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 X X 0 X 0 0 0 X X X 0 0 X 0 X X X X 0 0 0 X X X X X 0 0 0 0 0 X 0 X X X 0 X 0 X X 0 X 0 X X X X 0 0 0
0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 X 0 0 X 0 X 0 0 X 0 0 0 0 X X X 0 0 X X 0 X X X X 0 0 X X 0 0 X X X 0 X 0 X X 0 X X X 0 0 0 X 0 X 0 0 0
0 0 0 0 0 0 0 0 0 X 0 X X X X X 0 0 0 X 0 0 X X 0 0 X 0 X X 0 0 X X 0 X X 0 0 0 0 X 0 X 0 X 0 0 X X 0 0 X X 0 X 0 X 0 0 0 0 0 X 0 0 0
0 0 0 0 0 0 0 0 0 0 X X X X X 0 0 X X X X X 0 X 0 X 0 0 0 0 0 X 0 X 0 0 X 0 X X 0 0 X X 0 X X 0 0 X X X X X 0 0 0 X X 0 X X 0 0 0 0 0
generates a code of length 67 over Z2[X]/(X^2) who´s minimum homogenous weight is 52.
Homogenous weight enumerator: w(x)=1x^0+84x^52+53x^54+2x^55+146x^56+6x^57+128x^58+44x^59+179x^60+146x^61+141x^62+254x^63+178x^64+348x^65+139x^66+424x^67+133x^68+388x^69+169x^70+254x^71+133x^72+126x^73+170x^74+44x^75+101x^76+10x^77+123x^78+2x^79+53x^80+69x^82+15x^84+26x^86+1x^88+5x^90+1x^106
The gray image is a linear code over GF(2) with n=134, k=12 and d=52.
This code was found by Heurico 1.16 in 4.21 seconds.