The generator matrix

 1  0  0  1  1  1  X  1  1 X^2+X  1 X^2  1  1 X^2  1  X  1  1  X X^2+X  1  1  0  0  1  1  1  X X^2  X X^2+X  1  1  0  1 X^2+X  0  1  1  1  1  1  0  1
 0  1  0  X  1 X^2+X+1  1 X^2+X  0 X^2  1  1 X^2+X X^2+1  1 X+1  1 X^2+1 X^2+X+1  1 X^2+X X^2+X X^2  1  1  1 X^2 X^2+X  0  1  1  1  X  0  1 X^2  1 X^2+X X^2 X^2 X^2 X^2+1 X^2+1  1  0
 0  0  1  1 X^2+X+1 X^2+X  1 X+1 X^2+X  1  1  1  0  0  X X+1 X^2+X  1 X^2  1  1 X^2+X  1 X+1 X+1  X  1  0  1  X X^2+X+1  X  1 X+1 X^2+X X^2+X X^2+X  1  0 X^2+1 X^2+1 X+1 X^2+X+1  X X^2+X
 0  0  0 X^2  0  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0
 0  0  0  0 X^2  0  0  0  0  0 X^2  0  0  0  0 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2
 0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2
 0  0  0  0  0  0 X^2  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  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 38.

Homogenous weight enumerator: w(x)=1x^0+94x^38+240x^39+474x^40+332x^41+940x^42+650x^43+1061x^44+676x^45+1104x^46+638x^47+906x^48+308x^49+392x^50+170x^51+106x^52+28x^53+26x^54+26x^55+10x^56+4x^58+4x^59+1x^60+1x^64

The gray image is a linear code over GF(2) with n=180, k=13 and d=76.
This code was found by Heurico 1.16 in 1.92 seconds.