The generator matrix

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

generates a code of length 55 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+414x^46+592x^47+1829x^48+1600x^49+3907x^50+3076x^51+6262x^52+4252x^53+7901x^54+5252x^55+8339x^56+4692x^57+6454x^58+3104x^59+3697x^60+1464x^61+1611x^62+452x^63+387x^64+84x^65+118x^66+4x^67+29x^68+4x^69+6x^70+5x^74

The gray image is a code over GF(2) with n=220, k=16 and d=92.
This code was found by Heurico 1.13 in 51.8 seconds.