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

generates a code of length 49 over Z2[X]/(X^4) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+180x^45+63x^46+196x^47+470x^48+290x^49+420x^50+212x^51+54x^52+100x^53+11x^54+40x^55+2x^56+6x^57+2x^58+1x^88

The gray image is a linear code over GF(2) with n=392, k=11 and d=180.
This code was found by Heurico 1.16 in 142 seconds.