The generator matrix

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

generates a code of length 81 over Z2[X]/(X^4) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+370x^78+268x^79+428x^80+144x^81+300x^82+200x^83+187x^84+16x^85+94x^86+12x^87+18x^88+4x^92+4x^94+1x^108+1x^120

The gray image is a linear code over GF(2) with n=648, k=11 and d=312.
This code was found by Heurico 1.16 in 1.38 seconds.