The generator matrix

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

generates a code of length 83 over Z2[X]/(X^3) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+110x^75+340x^76+372x^77+604x^78+566x^79+718x^80+546x^81+795x^82+600x^83+681x^84+430x^85+600x^86+480x^87+426x^88+256x^89+224x^90+136x^91+119x^92+44x^93+74x^94+16x^95+18x^96+14x^97+5x^98+10x^99+2x^101+2x^102+2x^103+1x^104

The gray image is a linear code over GF(2) with n=332, k=13 and d=150.
This code was found by Heurico 1.16 in 4.71 seconds.