The generator matrix

 1  0  0  1  1  1  2  1  1  2  1  1  0  0  X X+2  1  1  X  1  X  1  1  1  X  0  X  1  1  1 X+2  0  1  2  1 X+2  X  X  1  2  X  1  1  1  1  0  1  1  1  1  X  1  1
 0  1  0  2  3  1  1  0  3  1  2  1  1 X+2  X  0  X X+3  1 X+3  1  X X+2 X+1  1  X  1 X+3  X X+2  1  1 X+2  1  0 X+2  0  1  2  2 X+2 X+1  1  3 X+3  1 X+1 X+3  3  1  1  X  0
 0  0  1 X+3 X+1  2 X+1 X+2  3  3  1  X X+2  1  1  1  1  X  X  3  3  0 X+1  0  2  1 X+3 X+1  X  2 X+3  1 X+2 X+3  2  1  1  1 X+2  1  1 X+2  0  X  2  X  X  0 X+2 X+2  0  2 X+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+65x^50+120x^51+92x^52+52x^53+44x^54+60x^55+17x^56+12x^57+17x^58+12x^59+18x^60+1x^62+1x^78

The gray image is a code over GF(2) with n=212, k=9 and d=100.
This code was found by Heurico 1.16 in 0.0435 seconds.