The generator matrix

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

generates a code of length 53 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+350x^48+224x^50+496x^52+256x^54+592x^56+32x^58+80x^60+15x^64+2x^80

The gray image is a code over GF(2) with n=212, k=11 and d=96.
This code was found by Heurico 1.16 in 0.266 seconds.