The generator matrix

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

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+88x^47+212x^48+396x^49+477x^50+584x^51+575x^52+716x^53+450x^54+264x^55+167x^56+100x^57+29x^58+24x^59+5x^60+4x^61+1x^62+1x^70+2x^74

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 6.67 seconds.