The generator matrix

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

generates a code of length 45 over Z2[X]/(X^4) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+52x^40+80x^41+136x^42+128x^43+446x^44+288x^45+612x^46+64x^47+99x^48+80x^49+48x^50+9x^52+4x^54+1x^84

The gray image is a linear code over GF(2) with n=360, k=11 and d=160.
This code was found by Heurico 1.16 in 0.125 seconds.