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

generates a code of length 45 over Z2[X]/(X^3) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+147x^36+339x^38+40x^39+605x^40+176x^41+861x^42+472x^43+1123x^44+672x^45+1131x^46+472x^47+906x^48+176x^49+576x^50+40x^51+263x^52+143x^54+23x^56+19x^58+3x^60+3x^62+1x^64

The gray image is a linear code over GF(2) with n=180, k=13 and d=72.
This code was found by Heurico 1.16 in 3.32 seconds.