The generator matrix

 1  0  0  1  1  1  0  1  1 X^2  1  X  1  1  0 X^2+X X^2+X  1 X^2+X  1  1 X^2 X^2+X  1  1  0  1  X  1  1  1  X  1  1  1  0  1  X X^2+X X^2+X  1  1  1  0  1  1  1  1  1  X  0 X^2 X^2+X X^2+X X^2+X  1  1 X^2 X^2+X  1  1  0  1  0  1  1  X  1  1 X^2  1  1  1  0  1  X  1 X^2  1 X^2+X  1 X^2+X X^2
 0  1  0  0  1  1  1 X^2  1  1 X+1 X^2+X X^2+X+1  X  1  1  1  X  0  X X+1  1  1  1 X^2 X^2+X X^2+X+1  1  0 X^2 X^2+1  1 X^2+X X+1  X  1 X^2+X+1  0  X  1 X^2+X+1 X^2+X  X  X X^2+X X+1 X+1 X^2+X X^2+1 X^2  1  0  X  1  1 X^2 X^2+X  1  1 X^2+X+1 X+1  1 X+1  1 X^2+1 X^2+X  1 X+1 X^2+1 X^2+X  0  1  X  1 X+1 X^2  0  1 X^2+X  1 X^2+X  0  1
 0  0  1 X+1 X^2+X+1  0 X+1  X  1  X  0  1  X  1 X^2+1  0 X+1  X  1 X^2+X+1 X^2+X+1  X X^2+1  X X^2+X  1  1 X+1 X^2+1  1 X^2+X X^2+X  0 X^2+1  X X^2  X  1  1 X^2 X^2  1  1  1  1 X+1  1  0 X^2+X+1  1  1  1  1  1 X^2+1 X^2  X X^2+X+1  0  0 X+1  X  X X+1 X^2+1 X^2  X  1 X^2+1  1 X^2+1 X^2 X^2+X+1 X^2+X X^2+X+1  1 X^2+X+1 X^2+X X^2 X^2 X^2  1 X^2+X+1
 0  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  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  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2
 0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0  0  0 X^2 X^2  0  0 X^2  0  0  0 X^2  0 X^2  0  0 X^2  0
 0  0  0  0  0 X^2  0  0  0  0  0  0  0  0  0  0 X^2 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0
 0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0 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+142x^75+214x^76+532x^77+428x^78+718x^79+515x^80+884x^81+468x^82+914x^83+521x^84+658x^85+355x^86+534x^87+234x^88+394x^89+166x^90+218x^91+88x^92+82x^93+48x^94+26x^95+18x^96+10x^97+6x^98+6x^99+9x^100+1x^102+2x^103

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 6.17 seconds.