The generator matrix

 1  0  0  0  1  1  1 X^2  1  1 X^2  1  0 X^2  1  1  0 X^2+X  1  1  X X^2+X  1  1  1  1  X  1 X^2+X X^2+X  1  1  1  X  X X^2  X  1 X^2  1  X  X  1  1  0 X^2+X X^2 X^2  1  1  1  1  1  0  0  1  1  0 X^2+X X^2+X  1 X^2  0  1  1  0 X^2  0 X^2+X X^2  X  1  X  1  1  X  1  X X^2 X^2+X  1
 0  1  0  0  X  X X^2+X  0  1 X^2+1  1  1  1  1 X^2+X+1 X^2+X X^2+X  1  0 X^2+X  1  0  0 X^2+1  1 X^2+1 X^2 X+1  1  0 X^2 X^2 X^2+1  1 X^2  1 X^2+X  1  1 X^2  1  1 X^2+X+1  X  0  0  X X^2+X  X X^2+1 X^2+1 X^2+X X^2+1  1  1 X+1  1  1  1  1 X^2  1  1 X^2 X^2+X+1  1 X^2 X^2+X  1  1  1 X^2+X+1  1  0 X^2+X  1 X^2+1  1  1  1 X+1
 0  0  1  0  X X^2+X+1 X^2+X+1  1 X+1 X+1 X^2  0 X+1 X^2+X+1  X X^2+X X^2+X X+1 X+1 X^2  1  1 X^2+X+1 X^2 X^2+1  1  1 X^2  0 X^2  1  X X^2+1  0  1  X  1  X X^2+1  X X+1 X^2+X X^2+1  0  1 X^2+X  1  1  X X+1  1  1 X^2 X^2 X^2+X+1  0 X+1  1 X^2+X X^2+1 X+1  1  1 X+1  1 X^2+1  1 X^2+X X^2+X+1  1  1 X+1 X^2+X+1 X+1 X^2+X+1  1  0 X^2 X^2+X X^2+1 X^2+X+1
 0  0  0  1 X+1 X^2+X+1  X  1  X X^2+X+1 X^2+X+1 X^2+X X^2+X  1  1 X^2  1 X^2+X+1 X^2+1 X+1 X^2+X X^2 X^2 X^2+1 X^2+1  0 X^2+X+1 X^2 X^2+X  1  1 X^2+1 X^2+X+1  1  X  X X^2+X+1 X+1 X^2+X X^2+X X+1  1  1  0 X^2+X  1  X X^2+X+1 X^2+1  0 X^2+X+1  1 X^2 X+1 X^2+X X^2+X+1 X^2 X^2+X+1 X+1  1 X^2 X^2+1 X^2+X+1 X+1  0  1  0  1  0 X^2+X+1 X+1  X  1 X^2+X  0  X X^2+X+1 X^2+X+1 X^2  0 X^2+X+1
 0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0  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+495x^74+1159x^76+1490x^78+1246x^80+1240x^82+935x^84+758x^86+460x^88+287x^90+97x^92+14x^94+5x^96+2x^98+1x^100+2x^102

The gray image is a linear code over GF(2) with n=324, k=13 and d=148.
This code was found by Heurico 1.16 in 60 seconds.