The generator matrix

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

generates a code of length 53 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+285x^50+280x^51+440x^52+240x^53+290x^54+216x^55+176x^56+32x^57+61x^58+20x^60+4x^62+2x^68+1x^72

The gray image is a code over GF(2) with n=424, k=11 and d=200.
This code was found by Heurico 1.16 in 0.109 seconds.