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

generates a code of length 45 over Z2[X]/(X^3) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+82x^35+172x^36+240x^37+326x^38+476x^39+684x^40+932x^41+1223x^42+1446x^43+1673x^44+1790x^45+1656x^46+1546x^47+1337x^48+882x^49+655x^50+496x^51+320x^52+230x^53+98x^54+50x^55+34x^56+18x^57+9x^58+2x^60+4x^61+1x^66+1x^76

The gray image is a linear code over GF(2) with n=180, k=14 and d=70.
This code was found by Heurico 1.16 in 14 seconds.