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

generates a code of length 53 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+138x^49+118x^50+390x^51+289x^52+332x^53+249x^54+244x^55+81x^56+130x^57+16x^58+30x^59+12x^60+8x^61+1x^62+8x^63+1x^84

The gray image is a code over GF(2) with n=424, k=11 and d=196.
This code was found by Heurico 1.16 in 0.187 seconds.