The generator matrix

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

generates a code of length 82 over Z2[X]/(X^3) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+244x^77+130x^78+354x^79+104x^80+310x^81+107x^82+220x^83+54x^84+148x^85+61x^86+118x^87+18x^88+42x^89+21x^90+56x^91+12x^92+20x^93+1x^94+20x^95+1x^96+4x^97+2x^100

The gray image is a linear code over GF(2) with n=328, k=11 and d=154.
This code was found by Heurico 1.16 in 15.1 seconds.