The generator matrix

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

generates a code of length 45 over Z2[X]/(X^3) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+124x^37+598x^38+1038x^39+1435x^40+1960x^41+2677x^42+2918x^43+3728x^44+3688x^45+3784x^46+3162x^47+2726x^48+1934x^49+1341x^50+830x^51+486x^52+176x^53+112x^54+32x^55+8x^56+6x^57+4x^59

The gray image is a linear code over GF(2) with n=180, k=15 and d=74.
This code was found by Heurico 1.13 in 8.55 seconds.