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  1  1  1  1  1  X  X  X  X  X  X  X  X  X  X  X  0  X  1  0  X  1  X  X  0  1  X  1  X  0  1  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  0  X  X  X  0  X  0  X  0  X  X  0  0  0  X  X  0  0  0  0  X  0  0  X  0  X  X  X  X  0  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  0  X  X  0  0  X  X  X  0  0  X  0  X  0  X  0  0  X  0  X  X  0  0  X  X  0  0  X  X  X  X  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  X  0  X  0  X  X  X  X  X  0  0  0  0  0  0  0  X  0  0  0  X  X  X  0  0  0  0  X  X  X  X  0  X  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  X  0  0  0  0  X  0  0  0  0  0  X  0  X  X  X  X  X  X  0  X  0  0  0  0  X  X  X  0  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  0  X  X  0  X  X  X  X  0  0  X  0  0  0  X  X  0  X  0  X  0  X  X  X  0  0  0  X  X  X  X  0  0  X  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  0  X  X  X  X  0  X  0  0  X  0  0  0  X  0  X  X  X  0  X  X  X  X  0  0  X  0  X  X  0  0  X  X  0  X
 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  X  X  X  X  0  X  X  X  X  0  0  X  X  X  0  X  X  0  0  X  0  X  0  X  0  X  0  X  0  X  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  0  X  X  X  X  0  X  X  X  X  0  X  X  0  0  0  0  X  X  0  0  0  X  X  X  X  0  0  0  0  X  0  X  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  0  0  X  0  X  0  X  X  0  X  0  X  X  0  X  0  X  0  0  X  0  0  X  0  X  X  0  0  0  X  X  0  0  X
 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  0  X  0  0  X  0  0  0  0  X  X  X  0  X  X  X  X  0  X  X  X  0  0  0  X  0  0  X  0  X  X  X  X  0  0

generates a code of length 77 over Z2[X]/(X^2) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+44x^62+97x^64+155x^66+212x^68+295x^70+391x^72+394x^74+470x^76+511x^78+448x^80+356x^82+220x^84+165x^86+127x^88+86x^90+54x^92+41x^94+21x^96+1x^98+4x^100+2x^104+1x^112

The gray image is a linear code over GF(2) with n=154, k=12 and d=62.
This code was found by Heurico 1.16 in 5.19 seconds.