The generator matrix

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

generates a code of length 54 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+166x^47+301x^48+464x^49+559x^50+698x^51+780x^52+732x^53+890x^54+822x^55+792x^56+638x^57+445x^58+360x^59+216x^60+130x^61+77x^62+58x^63+22x^64+18x^65+12x^66+6x^67+2x^69+1x^70+2x^71

The gray image is a code over GF(2) with n=216, k=13 and d=94.
This code was found by Heurico 1.16 in 3.01 seconds.