The generator matrix

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

generates a code of length 45 over Z2[X]/(X^3) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+272x^39+460x^40+706x^41+617x^42+796x^43+742x^44+1110x^45+767x^46+844x^47+587x^48+560x^49+281x^50+246x^51+90x^52+54x^53+29x^54+16x^55+8x^56+2x^57+2x^58+2x^59

The gray image is a linear code over GF(2) with n=180, k=13 and d=78.
This code was found by Heurico 1.16 in 44.9 seconds.