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

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+110x^44+96x^45+128x^46+320x^47+231x^48+96x^49+33x^52+8x^56+1x^84

The gray image is a linear code over GF(2) with n=376, k=10 and d=176.
This code was found by Heurico 1.16 in 23.1 seconds.