The generator matrix

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

generates a code of length 54 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+324x^52+120x^53+208x^54+48x^55+265x^56+24x^57+32x^58+1x^72+1x^80

The gray image is a code over GF(2) with n=432, k=10 and d=208.
This code was found by Heurico 1.16 in 0.562 seconds.