The generator matrix

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

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+48x^37+86x^38+136x^39+206x^40+234x^41+353x^42+398x^43+417x^44+444x^45+408x^46+366x^47+297x^48+256x^49+141x^50+106x^51+89x^52+36x^53+29x^54+18x^55+11x^56+6x^57+6x^58+2x^60+1x^62+1x^64

The gray image is a linear code over GF(2) with n=180, k=12 and d=74.
This code was found by Heurico 1.16 in 0.813 seconds.