The generator matrix

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

generates a code of length 90 over Z2[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+54x^78+54x^79+117x^80+130x^81+184x^82+198x^83+220x^84+224x^85+199x^86+232x^87+207x^88+246x^89+202x^90+206x^91+186x^92+200x^93+171x^94+168x^95+157x^96+150x^97+113x^98+138x^99+87x^100+56x^101+77x^102+24x^103+32x^104+18x^105+20x^106+2x^107+8x^108+3x^110+2x^111+5x^112+1x^114+3x^116+1x^120

The gray image is a linear code over GF(2) with n=180, k=12 and d=78.
This code was found by Heurico 1.16 in 4.06 seconds.