The generator matrix

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

generates a code of length 45 over Z2[X]/(X^4) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+208x^38+1064x^39+3123x^40+5272x^41+9965x^42+15366x^43+19603x^44+21604x^45+19843x^46+15602x^47+10360x^48+5016x^49+2545x^50+946x^51+343x^52+140x^53+41x^54+14x^55+8x^56+6x^58+2x^60

The gray image is a linear code over GF(2) with n=360, k=17 and d=152.
This code was found by Heurico 1.16 in 91.2 seconds.