The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1 X^2+X  1  1  1  0  1 X^2+X  1  1  1  0  1 X^2+X  1  1  1  1  X  1 X^2  1  1  1  1  1 X^2+X  1  0  1  1  1  1  1  0  1  0 X^2  1  1 X^2+X X^2+X  1  1  1 X^2  1  X  X  0  1  1  1 X^2  1  X  1  1  1  1  1  1 X^2+X  X  0  1  X  0 X^2+X  1  0 X^2
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X  1 X^2+1 X+1  0  1 X^2+X  1 X^2+1 X^2+1  0  1 X^2+X  1 X+1 X+1 X^2+1 X^2  1  1  1 X^2+X X+1  X X^2+X+1 X^2+1  1  0  1 X+1  1 X^2+X+1  1 X^2+X  1 X^2+X+1  1  1  0  1  1  1 X^2+X+1 X+1 X^2+1  1  X  1  0  1 X^2+1 X+1 X^2+X  X X^2  1 X^2+X X^2+X  X  0  0 X^2  1  1  1 X^2  1  1  1 X^2+X  1  1
 0  0 X^2  0  0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0  0  0  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2
 0  0  0 X^2  0  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0 X^2  0 X^2
 0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2
 0  0  0  0  0 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0  0  0  0  0 X^2 X^2  0  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2 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+57x^74+64x^75+195x^76+152x^77+223x^78+120x^79+203x^80+96x^81+174x^82+144x^83+182x^84+120x^85+161x^86+56x^87+46x^88+16x^89+19x^90+8x^92+2x^94+1x^96+1x^98+1x^100+2x^102+1x^104+1x^106+2x^108

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 0.572 seconds.