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

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+37x^48+58x^50+64x^51+707x^52+64x^53+60x^54+22x^56+10x^58+1x^100

The gray image is a code over GF(2) with n=416, k=10 and d=192.
This code was found by Heurico 1.16 in 0.125 seconds.