The generator matrix

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

generates a code of length 53 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+362x^50+255x^52+162x^54+83x^56+83x^58+74x^60+2x^64+1x^66+1x^68

The gray image is a code over GF(2) with n=212, k=10 and d=100.
This code was found by Heurico 1.16 in 11 seconds.