The generator matrix

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

generates a code of length 81 over Z2[X]/(X^3) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+150x^77+133x^78+140x^79+130x^80+98x^81+86x^82+92x^83+43x^84+36x^85+26x^86+16x^87+16x^88+18x^89+5x^90+12x^91+1x^92+8x^93+5x^94+4x^95+1x^96+1x^98+2x^101

The gray image is a linear code over GF(2) with n=324, k=10 and d=154.
This code was found by Heurico 1.11 in 0.265 seconds.