The generator matrix

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

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+22x^52+212x^54+14x^56+4x^58+3x^72

The gray image is a code over GF(2) with n=432, k=8 and d=208.
This code was found by Heurico 1.16 in 0.109 seconds.