The generator matrix

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

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+71x^38+250x^39+393x^40+582x^41+717x^42+820x^43+902x^44+836x^45+905x^46+836x^47+679x^48+508x^49+251x^50+196x^51+130x^52+52x^53+40x^54+10x^55+3x^56+6x^57+4x^60

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 2.18 seconds.