The generator matrix

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

generates a code of length 54 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+51x^44+78x^45+207x^46+350x^47+517x^48+640x^49+1014x^50+1258x^51+1435x^52+1800x^53+1751x^54+1820x^55+1519x^56+1158x^57+926x^58+684x^59+502x^60+268x^61+162x^62+102x^63+63x^64+18x^65+31x^66+10x^67+8x^68+6x^69+4x^70+1x^74

The gray image is a code over GF(2) with n=216, k=14 and d=88.
This code was found by Heurico 1.16 in 11.6 seconds.