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  X  1  1 2X+2  1  1  1  X  1 2X+2
 0  2  0 2X+2  0  0 2X+2  2  0  0 2X+2 2X+2 2X  0 2X+2  2 2X+2 2X  0 2X+2 2X  2 2X  2  0 2X+2 2X  0  2 2X  2  2  2  2 2X 2X 2X+2 2X  2  2  2 2X  0 2X+2  0  0 2X 2X  0  0  2  0
 0  0  2 2X+2  0  2 2X+2  0  2  0 2X+2 2X  0 2X+2  2 2X  0 2X+2  0  2 2X 2X+2 2X+2 2X  0 2X+2 2X+2 2X  0  2 2X 2X+2  2 2X+2 2X+2  2 2X  2  2 2X+2  0 2X+2  2 2X 2X+2  2  2  2 2X+2  2  0  2
 0  0  0 2X  0  0 2X  0  0 2X  0 2X 2X 2X  0  0  0  0  0 2X  0 2X 2X 2X 2X  0 2X 2X 2X 2X 2X  0 2X 2X  0  0  0  0 2X 2X  0 2X  0 2X  0 2X 2X 2X 2X 2X 2X  0
 0  0  0  0 2X  0 2X 2X 2X 2X  0 2X  0  0 2X 2X  0 2X  0 2X 2X  0 2X  0 2X 2X 2X  0  0  0 2X  0  0 2X  0 2X 2X  0 2X  0 2X  0  0 2X 2X 2X 2X 2X  0 2X 2X  0
 0  0  0  0  0 2X  0  0 2X 2X 2X 2X 2X  0 2X 2X 2X  0 2X 2X 2X 2X  0 2X  0  0 2X  0  0 2X  0  0  0 2X 2X  0 2X  0 2X  0 2X  0  0  0 2X  0  0 2X 2X  0  0  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+234x^48+256x^50+1088x^52+256x^54+200x^56+12x^64+1x^96

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 122 seconds.