The generator matrix

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

generates a code of length 47 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+344x^43+799x^44+1446x^45+994x^46+1484x^47+993x^48+980x^49+467x^50+328x^51+191x^52+118x^53+8x^54+36x^55+3x^58

The gray image is a code over GF(2) with n=376, k=13 and d=172.
This code was found by Heurico 1.16 in 0.5 seconds.