The generator matrix

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

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+232x^37+453x^38+1084x^39+1277x^40+2220x^41+2266x^42+3574x^43+3173x^44+4132x^45+3177x^46+3714x^47+2400x^48+2296x^49+1111x^50+874x^51+367x^52+268x^53+86x^54+34x^55+14x^56+4x^57+11x^58

The gray image is a linear code over GF(2) with n=180, k=15 and d=74.
This code was found by Heurico 1.16 in 25 seconds.