The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  X  1  1 X^2+X  1 X^2  1  1 X^2  1  1  1  1  1  1  X  1  X  X  1  1  1  1 X^2  1  1  0  1 X^2  1  0  1  1  X  1  0 X^2  1  1  0  1 X^2  1  1  X  1  X  1  1  1  1  1  1  X  0  1  1  1  1  X  0  X  1  1  1  1  1  1  1  1 X^2
 0  1  1 X^2+X X^2+X+1  1  0 X+1  1  X  1 X^2+1 X^2+X  1 X^2+X  1 X^2+X+1 X^2+X+1  1  0  1  1 X^2  0 X+1  1 X+1  1  1  0 X^2+X  1 X^2+1  1 X+1  X  1 X^2+1  1  1  1 X+1  X  1 X^2  1  1 X+1  0  1 X^2  1  1  1  1 X^2+X  1 X^2+X+1 X^2+X X^2+X+1 X+1  X  0  1  1 X+1  0 X+1  0 X^2  1  1 X^2 X+1 X^2+X X^2+X X+1 X^2+1 X+1 X^2  1
 0  0  X  0 X^2+X  0 X^2+X X^2  X  X  X X^2  0  0 X^2+X  X X^2+X  0 X^2 X^2  X X^2  X  X  X  0  0  X X^2+X  0  0 X^2+X X^2  X  X  X  0 X^2 X^2+X  X X^2 X^2 X^2+X X^2+X  X X^2+X  0 X^2  0  0  0  X X^2  X X^2+X X^2+X X^2+X  X  0  X  0  0 X^2 X^2  X  0  X  X  X  X X^2 X^2+X  X X^2+X  0  X  0 X^2+X X^2+X X^2 X^2+X
 0  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0
 0  0  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0
 0  0  0  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0  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 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0
 0  0  0  0  0  0 X^2  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2 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+246x^74+576x^76+668x^78+627x^80+677x^82+500x^84+506x^86+191x^88+48x^90+10x^92+16x^94+12x^96+13x^98+2x^102+1x^104+2x^108

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 75.9 seconds.