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

generates a code of length 92 over Z2[X]/(X^3) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+78x^81+143x^82+152x^83+252x^84+336x^85+371x^86+370x^87+459x^88+562x^89+614x^90+628x^91+616x^92+580x^93+481x^94+532x^95+455x^96+368x^97+294x^98+196x^99+169x^100+114x^101+96x^102+86x^103+80x^104+52x^105+39x^106+16x^107+15x^108+18x^109+7x^110+4x^111+1x^112+4x^113+2x^114+1x^126

The gray image is a linear code over GF(2) with n=368, k=13 and d=162.
This code was found by Heurico 1.16 in 9.25 seconds.