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

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

Homogenous weight enumerator: w(x)=1x^0+105x^48+258x^49+373x^50+526x^51+516x^52+720x^53+503x^54+426x^55+269x^56+166x^57+118x^58+46x^59+18x^60+24x^61+11x^62+10x^63+3x^64+2x^66+1x^82

The gray image is a code over GF(2) with n=424, k=12 and d=192.
This code was found by Heurico 1.16 in 0.328 seconds.