The generator matrix

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

generates a code of length 81 over Z2[X]/(X^2) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+26x^65+93x^66+224x^67+369x^68+438x^69+590x^70+742x^71+912x^72+1062x^73+1124x^74+1288x^75+1411x^76+1578x^77+1766x^78+1776x^79+1881x^80+1972x^81+1945x^82+1838x^83+1769x^84+1784x^85+1520x^86+1350x^87+1226x^88+1006x^89+805x^90+616x^91+483x^92+380x^93+276x^94+192x^95+122x^96+62x^97+62x^98+34x^99+16x^100+10x^101+8x^102+4x^103+2x^104+2x^106+2x^109+1x^122

The gray image is a linear code over GF(2) with n=162, k=15 and d=65.
This code was found by Heurico 1.11 in 70.2 seconds.