The generator matrix

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

generates a code of length 87 over Z2[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+74x^72+72x^73+199x^74+244x^75+323x^76+348x^77+453x^78+550x^79+622x^80+720x^81+789x^82+820x^83+828x^84+824x^85+867x^86+918x^87+874x^88+986x^89+819x^90+822x^91+741x^92+716x^93+563x^94+562x^95+407x^96+340x^97+287x^98+144x^99+143x^100+80x^101+95x^102+34x^103+68x^104+10x^105+18x^106+2x^107+12x^108+4x^110+2x^112+1x^116+2x^118

The gray image is a linear code over GF(2) with n=174, k=14 and d=72.
This code was found by Heurico 1.16 in 60.2 seconds.