The generator matrix

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

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