The generator matrix

 1  0  0  1  1  1  X X^2  1 X^2+X  1  1  1 X^2  1  1  0  1 X^2+X  0  1  0  1  1  X  1  1 X^2 X^2+X  1  1 X^2+X  1 X^2+X  1  1 X^2+X X^2  0 X^2  1  1 X^2+X X^2  1  1  1  0  1 X^2  1 X^2+X  1  1  1  1 X^2+X  1  1  1 X^2  1  1  X X^2+X  X  X  0 X^2+X  X  0  1  1  1  1  0  1  1 X^2+X X^2+X X^2  1
 0  1  0  0 X^2+1 X+1  1 X^2 X^2+X+1  1 X^2 X+1 X^2  1 X^2+X+1  0  1  1  0  1  0  1 X+1  1  1 X^2 X^2+X  X  X X^2+X X^2+X+1 X^2 X+1  1  0 X^2+X  1  1 X^2+X  1 X^2 X^2+X+1  1  1 X+1 X^2+X  X  1 X^2+X+1  1 X^2  1 X^2+1  X X^2  X X^2  X  X X^2+1  1  X X^2  1  1  1  1  0  1  1  1  0  X X^2+X X^2+X  1 X^2  1  X  1  1 X^2
 0  0  1  1 X^2+1 X^2 X^2+1  1 X^2+X+1  0 X+1 X^2  0  1 X^2+X+1 X+1  0 X^2  1  1 X^2 X^2  0 X^2+1  1  1  X  1  1  0 X^2+1  1 X^2+X X^2+X X^2+X  1 X^2+X+1  X  1 X^2+X  X X^2+1 X+1 X^2  X X^2+X  1 X^2+X+1 X^2+X X^2+X X^2+X+1 X^2+X+1 X^2+X+1 X+1 X^2+X X+1  1 X^2+1 X^2  X  1 X^2+X+1  X X^2+X+1  0 X^2+1  X  1  0 X^2+X X+1  1 X^2+X+1 X^2+1 X+1  X  X X+1  1 X^2+X  X X^2+X+1
 0  0  0  X  X  0  X  X  0  X  0 X^2+X X^2+X X^2 X^2+X X^2+X  X  0  0 X^2+X X^2 X^2  X X^2 X^2 X^2  X X^2+X X^2 X^2+X  X X^2+X  0  0 X^2  X  X X^2+X  0  0 X^2+X X^2 X^2 X^2+X X^2 X^2  0  X X^2+X  X X^2  0  0 X^2+X  X  0  X  0 X^2  X  0  X  0 X^2+X X^2+X  0 X^2 X^2+X X^2  X X^2  0  0 X^2+X X^2+X  0 X^2  X  0  X 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+238x^77+108x^78+368x^79+136x^80+288x^81+76x^82+232x^83+93x^84+166x^85+52x^86+114x^87+22x^88+48x^89+12x^90+20x^91+2x^92+24x^93+8x^94+34x^95+4x^97+1x^100+1x^112

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 0.892 seconds.