The generator matrix

 1  0  0  1  1  1 X^2+X X^3+X^2  1  1  0 X^3  1  1 X^3+X  1  1 X^3+X^2+X  X  1 X^3+X  1  1 X^2  1  1  1 X^3+X^2  1  1 X^3+X^2  1  1  1  1  1 X^2  1 X^3  1  1  1  1  1  1
 0  1  0  0  1 X^3+X+1  1  1 X^2+1 X^3+X  1 X^3+X X+1 X^2+X X^3 X^3+X^2+X+1  X  1  1 X^3+X  1 X+1 X^3+X^2  1 X^2 X^3+X^2  1  1 X^2+X+1 X^3+X^2  1 X^2+X+1  0  0 X^3+X^2+X+1 X^3+X^2+X  1 X+1  1  X  1 X^3+X^2+X+1 X^2+X X^3+X^2 X^3+X^2
 0  0  1  1  1 X^2+X  1 X^3+1 X^3+X X^3+1  0  1 X^2+1  X  1 X^3+X^2+X+1 X^3 X^2+X+1 X^2 X^3+X+1 X^3 X^3+X^2+X X^2 X^3+X^2+1 X^3+X^2+X+1 X^3+X X^2+X X^3+X^2+1 X^2  1 X^2+X X^3+X^2 X^3+X+1 X^3+X^2 X^2+1  X X^2+X+1 X^3+X^2+1  1 X^2 X^2+X+1 X^2+1 X^3 X^3 X^2
 0  0  0  X X^3 X^3+X X^3+X X^3+X^2 X^2 X^2 X^2+X X^3+X X^2+X  X  0 X^3+X X^3+X  X  0  0 X^3+X X^2 X^3+X  X  X X^3 X^3+X^2+X X^3 X^2  0 X^2 X^2+X X^3+X^2+X X^3+X^2  X X^2+X X^3  0 X^2+X X^3+X^2 X^3+X^2+X X^3+X^2 X^3  X X^2

generates a code of length 45 over Z2[X]/(X^4) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+100x^39+661x^40+1468x^41+2816x^42+3648x^43+4948x^44+5418x^45+5201x^46+3876x^47+2560x^48+1128x^49+595x^50+192x^51+83x^52+34x^53+23x^54+8x^55+2x^56+5x^58+1x^60

The gray image is a linear code over GF(2) with n=360, k=15 and d=156.
This code was found by Heurico 1.16 in 7.78 seconds.