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  1  1  1  1  1  1  1  1  1  1  1  0  0 X^2  X  0  1  1  X  1
 0  X  0  0  0  0  0  0  0  0 X^2  X  X X^2+X  0 X^2+X X^2+X  0  X  X X^2+X X^2+X X^2+X  X  X X^2 X^2  0  X  0  X  X X^2 X^2  X X^2  X  X  X X^2+X X^2  0 X^2+X X^2  X
 0  0  X  0  0  0  0  0  0  0 X^2+X X^2  X  X  X  X  0  X  0 X^2+X X^2+X  X X^2+X X^2 X^2 X^2+X  0 X^2  X X^2+X X^2  0 X^2  X  0 X^2+X X^2  0  0  0 X^2 X^2+X  X  X X^2
 0  0  0  X  0  0  0  X X^2+X  X  X X^2+X  0  X X^2  0 X^2+X X^2+X X^2+X X^2 X^2+X X^2 X^2+X  0 X^2 X^2+X  X  0  X  0  0 X^2  0  X  X  X  X  0 X^2+X  X X^2 X^2 X^2+X X^2  X
 0  0  0  0  X  0  X  X  X X^2  X  X  X X^2 X^2 X^2+X X^2+X X^2 X^2  0 X^2+X  0 X^2+X  0 X^2+X X^2+X  0 X^2+X X^2+X X^2+X  0  0  X  X  0  0 X^2 X^2  0  X  X  0  0  0 X^2
 0  0  0  0  0  X  X X^2 X^2+X X^2+X  X  X X^2+X  0  X X^2 X^2 X^2 X^2+X X^2 X^2+X  X  0  X X^2 X^2+X  0 X^2 X^2+X X^2+X  X X^2 X^2+X  0 X^2  X X^2+X X^2 X^2  0 X^2 X^2+X  0  0 X^2+X
 0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2 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 35.

Homogenous weight enumerator: w(x)=1x^0+80x^35+162x^36+210x^37+310x^38+372x^39+471x^40+642x^41+942x^42+1556x^43+2150x^44+2506x^45+2271x^46+1538x^47+987x^48+650x^49+460x^50+322x^51+294x^52+204x^53+106x^54+98x^55+29x^56+12x^57+6x^58+2x^59+2x^60+1x^78

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 11.9 seconds.