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

generates a code of length 86 over Z2[X]/(X^2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+31x^74+48x^75+116x^76+140x^77+187x^78+202x^79+206x^80+226x^81+217x^82+224x^83+216x^84+216x^85+215x^86+194x^87+202x^88+224x^89+183x^90+228x^91+155x^92+136x^93+119x^94+98x^95+78x^96+62x^97+39x^98+28x^99+34x^100+20x^101+21x^102+2x^103+8x^104+10x^106+7x^108+2x^110+1x^112

The gray image is a linear code over GF(2) with n=172, k=12 and d=74.
This code was found by Heurico 1.16 in 3.85 seconds.