The generator matrix

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

generates a code of length 51 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+408x^47+831x^48+1328x^49+1184x^50+1368x^51+967x^52+776x^53+488x^54+464x^55+210x^56+104x^57+24x^58+32x^59+5x^60+1x^64+1x^72

The gray image is a code over GF(2) with n=408, k=13 and d=188.
This code was found by Heurico 1.16 in 0.547 seconds.