The generator matrix

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

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+133x^40+188x^42+96x^43+500x^44+320x^45+390x^46+96x^47+213x^48+50x^50+44x^52+10x^54+4x^56+2x^58+1x^72

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.