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

generates a code of length 46 over Z2[X]/(X^4) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+24x^45+78x^46+15x^48+8x^49+2x^54

The gray image is a linear code over GF(2) with n=368, k=7 and d=180.
This code was found by Heurico 1.16 in 0.063 seconds.