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 X^2+2  1  1  1  X  1  1  1  1  1  1  1  0  1  2  1  0  X  1  X  2 X^2  1  0  X  1  2  1  1  1
 0  X  0  X  2  0 X^2+X X^2+X+2  0  2 X+2 X+2  0 X^2+X+2 X^2+2  X X^2+2 X^2+X X^2+X+2  2 X^2+X X+2  X X^2 X^2 X^2 X^2+X  0 X^2+X+2  X X^2 X+2 X^2+X+2 X^2 X^2+2 X^2+X+2 X^2  0  X X^2 X+2 X^2+X+2  X  X X+2  X X^2+X+2 X+2  X X+2  X  2
 0  0  X  X  0 X^2+X+2 X^2+X  2 X^2 X^2+X+2 X^2+X+2 X^2 X^2+2 X^2  X  X X^2+X+2 X+2  X X^2+2  0  2 X^2+2 X+2  0  0 X^2+X+2  X  0  X X+2 X^2 X^2+X+2 X^2  X X^2+X  X X+2 X^2+X+2 X^2+X+2  2  0 X^2+2  2 X^2+2  X X^2+X X^2+X X^2+2  X X^2+2  0
 0  0  0 X^2 X^2+2 X^2  2 X^2 X^2  0 X^2 X^2+2  0  0 X^2+2  2 X^2 X^2+2  2  2  2 X^2 X^2+2  2 X^2  0  0  2 X^2+2 X^2+2 X^2  2  0  0 X^2 X^2+2  2 X^2  0  0  2 X^2  0 X^2+2  0 X^2 X^2  2  2  0 X^2+2 X^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+166x^47+211x^48+312x^49+470x^50+620x^51+756x^52+480x^53+415x^54+294x^55+129x^56+112x^57+36x^58+56x^59+22x^60+8x^61+7x^62+1x^80

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.