The generator matrix

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

generates a code of length 45 over Z2[X]/(X^4) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+280x^41+943x^42+1138x^43+1389x^44+1176x^45+1269x^46+738x^47+581x^48+394x^49+197x^50+36x^51+29x^52+6x^53+7x^54+8x^55

The gray image is a linear code over GF(2) with n=360, k=13 and d=164.
This code was found by Heurico 1.16 in 1.66 seconds.