The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  X  1  1  1  X  1  1 X^2+X  1  0  1  1  1  0  0  1  1  1  0 X^2  1  1  1  1  1  X  X  1  1  1  0 X^2+X  1  1  1
 0  1  1  0 X^2+X+1  1  X X+1  1 X^2+X  1 X^2+1 X^2+X+1  0  1 X+1  X  1 X^2+1  1 X^2  1 X^2+X+1  1  1 X^2+1  0  0  1  1 X^2  1  0 X^2+X X+1  1  1  1 X^2+X+1 X^2  1  1  0 X^2+1  0
 0  0  X  0 X^2+X  0  0  X X^2  0 X^2  X  0 X^2+X X^2+X  0 X^2+X  X X^2 X^2+X  X X^2  X  X  X  X  0 X^2+X X^2  0 X^2+X  0 X^2  X  X  0  X X^2 X^2+X  X X^2 X^2+X  0 X^2  X
 0  0  0  X  0  0  X  X X^2+X X^2  X  X X^2+X  X  0 X^2 X^2  X X^2  0  0 X^2+X  X  0 X^2+X X^2  0  X X^2 X^2 X^2+X  X X^2+X X^2  X X^2+X  X  X X^2 X^2  X  X X^2  0 X^2+X
 0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 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  0  0  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0
 0  0  0  0  0  0 X^2  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2  0  0  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+85x^38+202x^39+346x^40+546x^41+710x^42+814x^43+939x^44+900x^45+924x^46+840x^47+675x^48+504x^49+294x^50+160x^51+72x^52+44x^53+31x^54+30x^55+10x^56+6x^57+4x^58+2x^59+5x^60

The gray image is a linear code over GF(2) with n=180, k=13 and d=74.
This code was found by Heurico 1.16 in 2.52 seconds.