The generator matrix

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

generates a code of length 52 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+92x^48+444x^49+706x^50+854x^51+566x^52+416x^53+313x^54+308x^55+144x^56+116x^57+84x^58+38x^59+12x^60+1x^62+1x^72

The gray image is a code over GF(2) with n=416, k=12 and d=192.
This code was found by Heurico 1.16 in 0.156 seconds.