The generator matrix

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

generates a code of length 52 over Z4[X]/(X^3+2,2X) 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 6.63 seconds.