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

generates a code of length 72 over Z2[X]/(X^2) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+52x^58+68x^59+192x^60+262x^61+386x^62+434x^63+513x^64+620x^65+707x^66+772x^67+822x^68+868x^69+862x^70+978x^71+1036x^72+1082x^73+1016x^74+1056x^75+854x^76+786x^77+675x^78+582x^79+489x^80+368x^81+301x^82+180x^83+160x^84+96x^85+76x^86+22x^87+22x^88+10x^89+18x^90+4x^91+3x^92+4x^93+1x^94+3x^96+2x^98+1x^108

The gray image is a linear code over GF(2) with n=144, k=14 and d=58.
This code was found by Heurico 1.16 in 89 seconds.