The generator matrix

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

generates a code of length 81 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+50x^76+96x^77+158x^78+92x^79+156x^80+96x^81+96x^82+36x^83+75x^84+28x^85+50x^86+16x^87+33x^88+20x^89+12x^90+3x^92+2x^104+4x^106

The gray image is a linear code over GF(2) with n=324, k=10 and d=152.
This code was found by Heurico 1.16 in 0.333 seconds.