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 X^2  1  1  1  X  1 X^2
 0 X^2+2  0 X^2  0  0 X^2 X^2+2  0  0 X^2 X^2  2  0 X^2 X^2+2 X^2  2  0 X^2  2 X^2+2  2 X^2+2  0 X^2  2  0 X^2+2  2 X^2+2 X^2+2 X^2+2 X^2+2  2  2 X^2  2 X^2+2 X^2+2 X^2+2  2  0 X^2  0  0  2  2  0  0 X^2+2  0
 0  0 X^2+2 X^2  0 X^2+2 X^2  0 X^2+2  0 X^2  2  0 X^2 X^2+2  2  0 X^2  0 X^2+2  2 X^2 X^2  2  0 X^2 X^2  2  0 X^2+2  2 X^2 X^2+2 X^2 X^2 X^2+2  2 X^2+2 X^2+2 X^2  0 X^2 X^2+2  2 X^2 X^2+2 X^2+2 X^2+2 X^2 X^2+2  0 X^2+2
 0  0  0  2  0  0  2  0  0  2  0  2  2  2  0  0  0  0  0  2  0  2  2  2  2  0  2  2  2  2  2  0  2  2  0  0  0  0  2  2  0  2  0  2  0  2  2  2  2  2  2  0
 0  0  0  0  2  0  2  2  2  2  0  2  0  0  2  2  0  2  0  2  2  0  2  0  2  2  2  0  0  0  2  0  0  2  0  2  2  0  2  0  2  0  0  2  2  2  2  2  0  2  2  0
 0  0  0  0  0  2  0  0  2  2  2  2  2  0  2  2  2  0  2  2  2  2  0  2  0  0  2  0  0  2  0  0  0  2  2  0  2  0  2  0  2  0  0  0  2  0  0  2  2  0  0  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+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 121 seconds.