The generator matrix

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

generates a code of length 45 over Z2[X]/(X^3) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+40x^38+108x^39+223x^40+234x^41+506x^42+330x^43+524x^44+260x^45+569x^46+296x^47+455x^48+156x^49+136x^50+116x^51+68x^52+20x^53+22x^54+12x^55+9x^56+2x^57+6x^58+2x^59+1x^62

The gray image is a linear code over GF(2) with n=180, k=12 and d=76.
This code was found by Heurico 1.16 in 0.541 seconds.