The generator matrix

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

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+86x^75+151x^76+242x^77+229x^78+154x^79+178x^80+180x^81+170x^82+106x^83+127x^84+134x^85+83x^86+50x^87+45x^88+32x^89+28x^90+16x^91+7x^92+14x^93+2x^94+4x^95+2x^96+4x^97+2x^101+1x^116

The gray image is a linear code over GF(2) with n=324, k=11 and d=150.
This code was found by Heurico 1.16 in 0.623 seconds.