The generator matrix

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

generates a code of length 81 over Z2[X]/(X^4) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+86x^77+292x^78+294x^79+294x^80+258x^81+232x^82+212x^83+192x^84+86x^85+74x^86+22x^87+1x^90+2x^97+1x^112+1x^114

The gray image is a linear code over GF(2) with n=648, k=11 and d=308.
This code was found by Heurico 1.16 in 0.625 seconds.