The generator matrix

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

generates a code of length 47 over Z2[X]/(X^4) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+522x^44+656x^45+849x^46+628x^47+492x^48+256x^49+328x^50+164x^51+130x^52+24x^53+39x^54+7x^56

The gray image is a linear code over GF(2) with n=376, k=12 and d=176.
This code was found by Heurico 1.16 in 5.95 seconds.