The generator matrix

 1  0  0  1  1  1 X^2+X  X  1  1  1  X  1  0 X^2  1  1  1 X^2  1 X^2  1  1  1 X^2+X X^2+X  1  1  X  1 X^2  0 X^2+X  1  1  1  X  1 X^2  0  0 X^2+X  1  1  1  1  1  1  1  1 X^2+X  0  1  1 X^2 X^2  1  1  X  1  0  X  1  1 X^2  1  1  0  1  1  0  X  0 X^2+X  0  1  1  1  1  1  1
 0  1  0  0  1 X+1  1 X^2  1 X^2+X+1  X  1 X^2+X  1  X X^2+X+1 X^2+1 X^2  1 X+1  1 X^2+X X^2+X X^2+X+1  1  1  0 X^2+1  0 X+1  1  1  X X^2+X X^2+X X^2+X+1  1  X  1 X^2+X X^2  1 X^2+X X^2 X^2+X+1 X^2  1 X^2  1 X^2 X^2  0 X^2+X  1  1  1  1  X  X X+1  1  1  1  X  0  X X+1  1 X^2  0  1  1  X  1  0 X^2+X+1  0  X X^2+X+1  X  0
 0  0  1  1  1 X^2  1  1 X+1  X X^2+X  X X^2+1  1  1 X+1  X  0  1 X^2+1 X^2 X^2+1 X^2  X X^2+X X^2+1 X^2+X+1 X+1  1 X^2 X^2+X+1  0  1  0 X^2+X X^2+X+1 X^2+X  0 X^2+X+1  1  1 X^2+X+1  X X+1 X+1  0  1  1 X^2+X+1  1  1  1 X^2+X+1 X^2+1 X+1 X^2+X+1  X  X  1 X^2+1  0  0 X^2+X+1 X^2+1  1  0 X^2 X^2+1 X^2+X  0  1 X+1  1 X^2  1 X+1 X+1 X^2  1 X^2+1  0
 0  0  0  X X^2+X  0  X  X  X X^2 X^2 X^2  X  X  X  X X^2+X  X X^2  0 X^2+X X^2  X X^2+X X^2+X X^2 X^2 X^2 X^2 X^2  X  0 X^2+X X^2+X X^2+X  0 X^2 X^2  0 X^2 X^2+X  X  X X^2+X  0 X^2 X^2+X X^2 X^2+X  X  0  X X^2 X^2 X^2  0 X^2  X  X X^2+X X^2+X  0  0  X X^2 X^2 X^2+X  0  0 X^2+X X^2+X X^2  X X^2 X^2 X^2  X  X X^2 X^2  0
 0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0 X^2  0  0  0 X^2 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 74.

Homogenous weight enumerator: w(x)=1x^0+70x^74+176x^75+347x^76+352x^77+450x^78+342x^79+457x^80+280x^81+333x^82+194x^83+207x^84+174x^85+198x^86+138x^87+106x^88+80x^89+73x^90+46x^91+43x^92+8x^93+11x^94+7x^100+2x^101+1x^102

The gray image is a linear code over GF(2) with n=324, k=12 and d=148.
This code was found by Heurico 1.16 in 1.23 seconds.