The generator matrix

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

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+126x^41+639x^42+1752x^43+2476x^44+3820x^45+4987x^46+5494x^47+4884x^48+3864x^49+2297x^50+1368x^51+594x^52+290x^53+97x^54+42x^55+21x^56+10x^57+4x^58+2x^61

The gray image is a linear code over GF(2) with n=376, k=15 and d=164.
This code was found by Heurico 1.16 in 8.88 seconds.