The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  0 X^2  X  1  X  1 X^2  X  0  0  1  X X^2  0  1  0  1  1  X  1  1  0  1  1  0  X  1  1  0  1  0  1  1  X  1  1  0  0 X^2  X  0  1  0  1  1
 0  X  0  0  0  0  0  0  0 X^2+X  X  X  X  X X^2+X X^2+X  X X^2  X  0  X X^2  0 X^2+X  X X^2  X X^2+X X^2 X^2 X^2 X^2+X X^2+X X^2  0 X^2+X  0 X^2  0  0  X  X  0 X^2 X^2+X  0 X^2+X X^2+X  X  X X^2  X X^2 X^2+X  X X^2  0  X  0 X^2+X X^2 X^2 X^2 X^2  0  X  X  X X^2 X^2+X  0  0 X^2 X^2+X  X  X X^2+X X^2  0  X  X  0 X^2  0  X  X  0
 0  0  X  0  0  0  X X^2+X  X X^2  X X^2+X  0  0  X X^2+X X^2 X^2 X^2  X X^2  X X^2  X X^2+X  X  X X^2+X X^2  X  0  0  0 X^2+X  X X^2  X X^2  X X^2  0 X^2 X^2  X X^2 X^2  0 X^2+X  0 X^2+X  0  0  0  X X^2+X  X X^2 X^2+X  X  0  0 X^2 X^2  X X^2+X X^2+X  X X^2+X X^2+X X^2+X  X  0 X^2 X^2  0 X^2 X^2+X X^2+X  0  0 X^2 X^2+X  X X^2+X X^2+X  0 X^2+X
 0  0  0  X  0  X  X  X  0 X^2+X X^2  X X^2+X  0  0 X^2+X X^2+X X^2+X  X X^2+X  0 X^2 X^2  X  0  X  0  X X^2  X  X  X  0  0 X^2 X^2+X  0 X^2 X^2+X  X X^2  X  0 X^2  X  X X^2+X  0  0  0  X  0  0 X^2  X  X X^2 X^2 X^2 X^2 X^2  0  0  0 X^2+X X^2+X X^2 X^2+X  X  X  0 X^2+X X^2  0  X  0  X X^2+X  X  X  0 X^2 X^2 X^2+X X^2+X  X X^2
 0  0  0  0  X  X  0  X X^2+X  X  0  X X^2 X^2+X  X X^2 X^2  0 X^2+X  X X^2  0 X^2  X  0 X^2+X  X  0 X^2 X^2 X^2+X X^2 X^2+X X^2 X^2+X X^2+X  X  X  0 X^2+X X^2 X^2  X  X  X X^2+X X^2+X  0  X X^2  0  0 X^2+X  0 X^2  0  X  0  0  X X^2+X X^2 X^2  0 X^2 X^2+X X^2+X  X X^2 X^2+X  0 X^2+X  X  0 X^2+X  0  0  0 X^2+X  X  0 X^2+X  X  X  0  0  X
 0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2
 0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2

generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+57x^76+110x^77+155x^78+228x^79+302x^80+378x^81+399x^82+478x^83+572x^84+610x^85+673x^86+658x^87+577x^88+544x^89+507x^90+464x^91+349x^92+252x^93+205x^94+146x^95+135x^96+116x^97+75x^98+56x^99+46x^100+28x^101+31x^102+16x^103+9x^104+10x^105+2x^106+2x^107+1x^122

The gray image is a linear code over GF(2) with n=348, k=13 and d=152.
This code was found by Heurico 1.16 in 8.57 seconds.