The generator matrix

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

generates a code of length 45 over Z2[X]/(X^3) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+52x^34+66x^35+190x^36+192x^37+347x^38+486x^39+774x^40+924x^41+1049x^42+1432x^43+1854x^44+1836x^45+1319x^46+1680x^47+1364x^48+932x^49+650x^50+374x^51+339x^52+196x^53+149x^54+58x^55+74x^56+16x^57+17x^58+8x^60+1x^62+3x^64+1x^68

The gray image is a linear code over GF(2) with n=180, k=14 and d=68.
This code was found by Heurico 1.16 in 11.7 seconds.