The generator matrix

 1  0  0  0  1  1  1  0  1  1  X  1  0  1  0  X  X  X  1  1  X  1  0  1  X  1  1  1  1  0  1  0  1  X  1  1  X  X  0  X  1  1  1  1  1  X  1  0  X  0  X  X  0  X  1  1  X  1  1  1  1  1  X  1  1  1  1  1  0  X  X  0  X  X  1  1  1  1  1  1  1  0  1  1  1  0  1  0  1  0
 0  1  0  0  0  0  0  0  1 X+1  1 X+1  1  1  1  1  X  0 X+1  X  1  X  1  1  1  0 X+1  1  1  0  1  X  X  1  1  0  X  0  1  X  1  0 X+1  X  1  1 X+1  1  1  0  1  X  1  1  X  X  1 X+1  X X+1  X  X  1  X  X X+1  1  X  1  0  0  1  1  X X+1  X X+1 X+1  1  1  0  0  X X+1 X+1  1  0  0 X+1  X
 0  0  1  0  0  1  1  1  1  1  X  0  1  0 X+1  X  0  1 X+1  0  X X+1  1 X+1 X+1  0  0 X+1 X+1  1  X  X  X  X  0 X+1  1  1  1  1  X  1  0  0  1 X+1  1  X  1  1  0  1  0 X+1  1  0  X  1  0  1  1 X+1  X  X  1  1 X+1  0  X  1  1  1  0  0  1 X+1  1  1 X+1 X+1  X  X  X X+1  1 X+1  1  X  0  1
 0  0  0  1  1  1  0  1  X X+1 X+1  0  X  1  1  X  1  X  X  1 X+1 X+1 X+1 X+1  X  X  0 X+1  0  0 X+1  1  1 X+1  1  0 X+1  1  X  1  0 X+1 X+1  0  0 X+1  0  0 X+1  X  0  X  0 X+1 X+1  X  0  0  0 X+1 X+1  X  0 X+1 X+1  0  1  0  X  X  0  0  1  1  0 X+1  1  1  X X+1  1  1 X+1  0 X+1  X  1  1  X  1
 0  0  0  0  X  0  0  0  X  X  X  X  X  X  0  0  X  X  0  0  0  0  0  X  0  X  X  0  0  0  X  0  X  X  0  X  0  X  X  0  X  X  0  0  0  X  0  X  0  X  X  0  0  0  0  X  X  0  X  X  0  X  0  X  0  X  0  X  X  X  0  X  0  X  X  X  0  X  0  0  0  X  X  X  0  X  X  X  0  X
 0  0  0  0  0  X  0  0  0  0  0  X  0  X  0  X  0  X  0  X  0  X  X  0  0  X  0  X  0  X  X  X  X  0  0  X  0  X  X  0  X  0  X  0  X  0  X  X  X  X  0  X  0  0  0  0  0  X  0  X  0  0  0  0  X  0  0  X  X  0  0  X  0  X  0  X  0  X  X  X  0  0  X  0  0  X  X  X  X  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  0  X  X  0  X  0  X  0  0  X  X  X  X  X  0  X  0  0  0  X  X  X  0  X  0  X  X  0  X  0  X  X  X  0  X  X
 0  0  0  0  0  0  0  X  X  0  0  0  0  0  X  0  X  X  0  X  0  X  X  X  0  X  0  0  X  X  X  0  X  X  0  X  X  0  X  0  0  0  0  0  0  X  X  X  X  0  X  0  X  X  X  X  0  X  0  0  0  0  X  X  X  X  0  0  0  X  X  0  X  0  0  0  X  X  0  0  0  0  X  0  X  X  0  0  X  X

generates a code of length 90 over Z2[X]/(X^2) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+50x^79+112x^80+166x^81+206x^82+200x^83+225x^84+236x^85+233x^86+260x^87+220x^88+192x^89+198x^90+212x^91+204x^92+164x^93+174x^94+140x^95+129x^96+164x^97+136x^98+94x^99+87x^100+82x^101+51x^102+50x^103+34x^104+14x^105+20x^106+14x^107+12x^108+6x^109+6x^110+4x^111

The gray image is a linear code over GF(2) with n=180, k=12 and d=79.
This code was found by Heurico 1.16 in 4.56 seconds.