The generator matrix

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

generates a code of length 81 over Z2[X]/(X^3) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+216x^75+300x^76+450x^77+385x^78+460x^79+352x^80+364x^81+265x^82+308x^83+166x^84+178x^85+133x^86+136x^87+80x^88+72x^89+79x^90+86x^91+18x^92+24x^93+2x^94+8x^95+11x^96+2x^99

The gray image is a linear code over GF(2) with n=324, k=12 and d=150.
This code was found by Heurico 1.16 in 1.36 seconds.