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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^3  1  1  1  1  1  1  1  1  0  X  1  1  0 X^3  1  1  1
 0  X  0 X^3+X^2+X X^3 X^2+X  0  X X^2 X^2+X X^3+X^2  X X^2 X^3+X X^2 X^2+X  0 X^3+X^2+X X^2 X^3+X^2+X X^3 X^2+X X^3  X  0  X  0  X X^3+X^2 X^3+X  X X^2 X^2 X^2+X X^2+X X^3+X^2 X^2 X^3+X  X X^3+X^2 X^3+X X^3+X^2 X^2  X X^3+X X^3+X^2 X^2+X X^3+X^2 X^2+X X^3+X^2+X  0  0  X X^3+X X^3  0 X^3 X^2+X X^3+X^2+X X^2+X X^3+X^2+X X^3+X^2 X^3 X^3  0 X^3+X^2 X^3+X^2  0 X^3+X^2 X^2 X^2 X^2  X X^3+X^2+X X^3+X^2+X X^3+X  X  X X^3  0 X^3
 0  0 X^3+X^2  0  0 X^3+X^2 X^2 X^2 X^2 X^3 X^3+X^2 X^3 X^3 X^2 X^3 X^3+X^2  0 X^2 X^3  0 X^3+X^2 X^2 X^2  0 X^3 X^3 X^3 X^2 X^3+X^2  0 X^3+X^2 X^3+X^2  0 X^3 X^2  0 X^2  0 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^3 X^3+X^2  0  0  0 X^3 X^3+X^2 X^3  0 X^3 X^2 X^3 X^2 X^3+X^2  0 X^2 X^3 X^3+X^2 X^3 X^3+X^2  0 X^2 X^3 X^3 X^3+X^2 X^2 X^2  0  0  0 X^3 X^3+X^2 X^3+X^2 X^2 X^2 X^2  0  0
 0  0  0 X^3+X^2 X^2 X^3+X^2 X^2  0  0  0 X^2 X^3+X^2 X^2 X^3+X^2  0  0 X^3  0 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^3 X^3+X^2 X^2 X^3+X^2  0  0 X^3+X^2 X^2 X^2 X^3+X^2 X^3  0 X^3 X^3 X^2 X^3  0 X^2 X^3+X^2 X^2 X^3 X^2 X^2 X^2 X^3+X^2 X^2 X^2  0 X^3 X^3+X^2 X^3 X^3 X^3 X^3  0 X^2  0  0 X^3 X^2 X^3 X^3+X^2 X^2 X^2 X^3  0 X^3+X^2 X^3+X^2  0 X^2  0  0 X^3 X^2

generates a code of length 81 over Z2[X]/(X^4) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+38x^76+72x^77+154x^78+312x^79+402x^80+368x^81+228x^82+144x^83+101x^84+72x^85+82x^86+56x^87+16x^88+1x^92+1x^152

The gray image is a linear code over GF(2) with n=648, k=11 and d=304.
This code was found by Heurico 1.16 in 0.656 seconds.