The generator matrix

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

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+230x^77+117x^78+346x^79+152x^80+360x^81+73x^82+202x^83+51x^84+150x^85+61x^86+88x^87+28x^88+54x^89+8x^90+62x^91+1x^92+32x^93+12x^94+6x^95+5x^96+6x^97+1x^98+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 1.11 in 0.578 seconds.