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

generates a code of length 54 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+117x^48+32x^50+256x^53+1216x^54+256x^55+83x^56+32x^58+53x^64+1x^72+1x^96

The gray image is a code over GF(2) with n=432, k=11 and d=192.
This code was found by Heurico 1.16 in 0.359 seconds.