The generator matrix

 1  0  0  1  1  1  0 X^2 X^2 X^2  1  1  1  1  X X^2+X  1  1 X^2  1 X^2  1  1  1 X^2+X  1  0  0  1 X^2+X  1  1  1  1  1  1  1  1  X X^2  1 X^2+X  1  1  1  1  1  X  1  0  1  X  0  0 X^2 X^2+X  X X^2 X^2 X^2  X  X X^2+X X^2+X  0 X^2+X X^2  X  X X^2  1  1  1  1 X^2+X  1  1 X^2+X  0  1  1
 0  1  0  0 X^2+1 X^2+1  1  X  1  1 X^2 X^2 X^2+1 X^2+1 X^2+X  0 X^2+X X^2+X+1  1 X^2  1 X^2 X+1 X^2+X+1 X^2  X  1  1 X+1  X  X X^2+X  0 X^2+1 X+1  0 X^2+1 X+1 X^2+X  1 X^2+X+1  X X^2+1 X^2+X+1 X^2+1 X^2+X  X X^2  X  1 X^2+X  0  1  X  1  1  1  0  X  X  1  1  1  1 X^2+X  1 X^2+X  1  1 X^2+X  0 X^2  0 X^2  1 X^2+X  X  1  1 X^2 X^2
 0  0  1 X+1 X^2+X+1 X^2 X^2+X+1  1  X  1  X X^2+1  1 X^2+X  1  1 X^2+X  0 X^2 X+1 X^2+X+1 X^2 X^2+X+1  X  1 X^2+1  1  X  1  1 X^2 X+1 X^2+X  X  1 X^2+1  0 X^2+X+1  1 X+1 X^2  1  1 X^2+X X^2+X+1 X^2+1 X+1  1  X  1  0  1 X+1 X^2+X  1 X+1 X^2+X+1  1  1  0  1 X^2+1 X+1 X^2+X  1  0  1  1 X^2+1  1  0 X^2+X+1 X^2 X^2+X+1 X^2+X X^2+X+1 X^2 X^2 X^2+X X^2+X  0
 0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2  0 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+126x^77+94x^78+200x^79+142x^80+124x^81+82x^82+84x^83+24x^84+50x^85+23x^86+20x^87+4x^89+3x^90+8x^91+16x^93+12x^94+8x^95+1x^96+1x^98+1x^102

The gray image is a linear code over GF(2) with n=324, k=10 and d=154.
This code was found by Heurico 1.16 in 0.322 seconds.