The generator matrix

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

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+174x^49+449x^50+732x^51+496x^52+776x^53+391x^54+396x^55+278x^56+198x^57+70x^58+80x^59+40x^60+12x^61+1x^62+1x^66+1x^72

The gray image is a code over GF(2) with n=424, k=12 and d=196.
This code was found by Heurico 1.16 in 0.265 seconds.