The generator matrix

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

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+65x^38+210x^39+466x^40+576x^41+725x^42+824x^43+793x^44+938x^45+879x^46+832x^47+678x^48+462x^49+339x^50+196x^51+99x^52+38x^53+36x^54+14x^55+11x^56+2x^57+4x^58+4x^59

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 2.14 seconds.