The generator matrix

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

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+184x^74+4x^75+77x^76+100x^77+208x^78+252x^79+80x^80+312x^81+136x^82+268x^83+58x^84+68x^85+132x^86+20x^87+30x^88+72x^90+8x^92+36x^94+1x^96+1x^140

The gray image is a linear code over GF(2) with n=324, k=11 and d=148.
This code was found by Heurico 1.16 in 7.11 seconds.