The generator matrix

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

generates a code of length 47 over Z2[X]/(X^4) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+274x^41+1482x^42+3458x^43+5248x^44+7606x^45+9109x^46+10750x^47+9839x^48+7838x^49+5124x^50+3026x^51+1110x^52+392x^53+197x^54+46x^55+16x^56+16x^57+2x^60+2x^61

The gray image is a linear code over GF(2) with n=376, k=16 and d=164.
This code was found by Heurico 1.16 in 31.9 seconds.