The generator matrix

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

generates a code of length 45 over Z2[X]/(X^4) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+2x^44+46x^45+2x^46+8x^47+2x^49+1x^50+1x^52+1x^54

The gray image is a linear code over GF(2) with n=360, k=6 and d=176.
This code was found by Heurico 1.16 in 0.047 seconds.