The generator matrix

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

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+238x^44+366x^45+371x^46+306x^47+239x^48+214x^49+175x^50+70x^51+53x^52+4x^53+5x^54+4x^56+1x^60+1x^66

The gray image is a linear code over GF(2) with n=376, k=11 and d=176.
This code was found by Heurico 1.16 in 0.5 seconds.