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

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

Homogenous weight enumerator: w(x)=1x^0+219x^48+28x^49+70x^50+208x^51+221x^52+268x^53+102x^54+288x^55+166x^56+212x^57+46x^58+16x^59+108x^60+4x^61+26x^62+46x^64+12x^66+6x^68+1x^84

The gray image is a code over GF(2) with n=216, k=11 and d=96.
This code was found by Heurico 1.16 in 6.47 seconds.