The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X  X  0  1 X^2  1 X^2  1  1  1  1  X  1  1  1  X  0  0  0  X X^2  1  X  1  1
 0  X  0  X  0  0  X X^2+X  0  0  X X^2+X X^2  0 X^2+X X^2+X X^2 X^2 X^2  0 X^2+X  X  X X^2+X  X  X  X  X  X X^2+X  0  0  0 X^2+X X^2 X^2+X  X  0  0 X^2  X  X  X X^2  0
 0  0  X  X  0 X^2+X  X  0  0 X^2+X  X  0  X X^2  X  0 X^2  X  X  X  0  X  0 X^2  X X^2+X  X X^2  X X^2 X^2 X^2+X X^2+X  0  0  0  0  X  X  X  X X^2 X^2+X  X  X
 0  0  0 X^2  0  0  0  0  0  0  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0
 0  0  0  0 X^2  0  0  0  0  0  0  0  0 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0
 0  0  0  0  0 X^2  0  0  0  0  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0  0  0 X^2  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 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  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2
 0  0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2
 0  0  0  0  0  0  0  0 X^2  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2
 0  0  0  0  0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2  0 X^2 X^2  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+69x^34+64x^35+168x^36+176x^37+291x^38+498x^39+621x^40+950x^41+1182x^42+1444x^43+1749x^44+1840x^45+1792x^46+1572x^47+1205x^48+972x^49+609x^50+456x^51+282x^52+144x^53+123x^54+58x^55+60x^56+14x^57+28x^58+4x^59+9x^60+2x^62+1x^72

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 14.3 seconds.