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

generates a code of length 52 over Z4[X]/(X^2+2X+2) who�s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+114x^47+250x^48+342x^49+573x^50+528x^51+689x^52+526x^53+398x^54+282x^55+157x^56+74x^57+65x^58+52x^59+31x^60+2x^61+11x^62+1x^78

The gray image is a code over GF(2) with n=416, k=12 and d=188.
This code was found by Heurico 1.16 in 0.328 seconds.