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 2X  X  2  X  X  0  X 2X+2  X  X  2  X  0  1  1  1  1  1  1  1  1
 0  X  0 3X+2  0 X+2  0 3X  2 X+2 2X+2  X  2 3X+2 2X+2 3X 2X X+2 2X  X 2X 3X+2 2X 3X 2X+2 3X+2  2 3X 2X+2 X+2  2  X X+2  X 3X  X 2X 3X+2  X  X  X  0  2 2X 2X+2  0  0  2 2X 2X+2 X+2 3X+2 3X  X
 0  0 2X+2  2 2X 2X+2  2 2X  2  0  0  2 2X+2 2X 2X 2X+2 2X 2X  2 2X+2  0  0 2X+2  2 2X+2 2X+2 2X  0  2  2  0 2X  0  2 2X 2X+2  2  2 2X  2  0  2  2 2X+2 2X+2  2  0 2X+2 2X  2  0 2X  0 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+90x^52+192x^53+96x^54+52x^56+64x^57+14x^60+2x^64+1x^80

The gray image is a code over GF(2) with n=432, k=9 and d=208.
This code was found by Heurico 1.16 in 0.125 seconds.