The generator matrix

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

generates a code of length 54 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+80x^43+418x^44+868x^45+1456x^46+2722x^47+4150x^48+5886x^49+7788x^50+9796x^51+11796x^52+13096x^53+13870x^54+13540x^55+12385x^56+10444x^57+8046x^58+5780x^59+3804x^60+2328x^61+1358x^62+738x^63+381x^64+206x^65+54x^66+48x^67+22x^68+4x^69+4x^70+3x^72

The gray image is a code over GF(2) with n=216, k=17 and d=86.
This code was found by Heurico 1.13 in 174 seconds.