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  2  X X^2  X  X  0  X X^2+2  X  X X^2  X  0  1  1  1  1  1  1  1  1
 0  X  0 X^2+X+2  0 X^2+X  0 X+2 X^2 X^2+X X^2+2  X X^2 X^2+X+2 X^2+2 X+2  2 X^2+X  2  X  2 X^2+X+2  2 X+2 X^2+2 X^2+X+2 X^2 X+2 X^2+2 X^2+X X^2  X X^2+X  X X+2  X  2 X^2+X+2  X  X  X  0 X^2  2 X^2+2  0  0 X^2  2 X^2+2 X^2+X X^2+X+2 X+2  X
 0  0 X^2+2 X^2  2 X^2+2 X^2  2 X^2  0  0 X^2 X^2+2  2  2 X^2+2  2  2 X^2 X^2+2  0  0 X^2+2 X^2 X^2+2 X^2+2  2  0 X^2 X^2  0  2  0 X^2  2 X^2+2 X^2 X^2  2 X^2  0 X^2 X^2 X^2+2 X^2+2 X^2  0 X^2+2  2 X^2  0  2  0  2

generates a code of length 54 over Z4[X]/(X^3+2,2X) 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.