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

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+37x^48+128x^49+64x^50+160x^51+225x^52+856x^53+229x^54+136x^55+41x^56+104x^57+23x^58+24x^59+15x^60+3x^62+1x^64+1x^98

The gray image is a code over GF(2) with n=424, k=11 and d=192.
This code was found by Heurico 1.16 in 0.172 seconds.