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

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+36x^41+42x^42+52x^43+220x^44+340x^45+208x^46+56x^47+31x^48+20x^49+6x^50+4x^51+3x^52+4x^53+1x^84

The gray image is a linear code over GF(2) with n=360, k=10 and d=164.
This code was found by Heurico 1.16 in 0.078 seconds.