The generator matrix

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

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+115x^48+188x^49+206x^50+404x^51+252x^52+372x^53+220x^54+172x^55+79x^56+16x^57+21x^58+1x^72+1x^74

The gray image is a code over GF(2) with n=416, k=11 and d=192.
This code was found by Heurico 1.16 in 0.109 seconds.