The generator matrix

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

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+483x^48+944x^50+790x^52+748x^54+512x^56+344x^58+194x^60+76x^62+4x^64

The gray image is a code over GF(2) with n=212, k=12 and d=96.
This code was found by Heurico 1.11 in 1.24 seconds.