The generator matrix

 1  0  0  0  1  1  1  1  X  1  0  1  2  X  1  1  1  1  2  1  2  1  1 X+2  1  0  X  1  2  1  1  2 X+2  1  X  1  2  1  1  1  1  1  2  X  0  0 X+2  1  1 X+2  1  1  1  1
 0  1  0  0  0  1  2  3  1  0  1  1  1  2  3  X  3  1  X  1  1  X X+2  1  3 X+2  X X+3 X+2 X+2  X  1  1 X+1  1 X+2  X X+2 X+3  3  3 X+1  1  1 X+2  2 X+2  0 X+1  X  X X+3 X+3  0
 0  0  1  0  1  2  0  3  1 X+1  X X+3  1  1  0 X+2 X+3 X+2 X+2 X+1  2  3  2  X X+2  1  0 X+3  1 X+2 X+1 X+3 X+1  1  1  1  0 X+2  0  1  X  2  X  0  1  1  X  X X+1  1  0 X+2  X  1
 0  0  0  1  2  0  1  3 X+3  3 X+3  X  X  3 X+3 X+2  0  2  1  1 X+1 X+1  2  2  1  1  1 X+1  2 X+1  X X+2  X X+3  1 X+2  1  1  X X+3 X+2  1  0 X+1 X+1  1  1  1  2  1 X+3 X+3  3 X+1

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+70x^48+294x^49+345x^50+500x^51+356x^52+482x^53+382x^54+346x^55+272x^56+342x^57+170x^58+220x^59+132x^60+70x^61+46x^62+34x^63+17x^64+12x^65+1x^66+4x^67

The gray image is a code over GF(2) with n=216, k=12 and d=96.
This code was found by Heurico 1.11 in 0.275 seconds.