The generator matrix

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

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+66x^44+44x^46+11x^48+4x^50+2x^52

The gray image is a linear code over GF(2) with n=360, k=7 and d=176.
This code was found by Heurico 1.16 in 0.063 seconds.