The generator matrix

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

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+46x^46+368x^47+837x^48+1102x^49+1626x^50+2140x^51+2459x^52+2902x^53+3113x^54+3460x^55+3273x^56+2914x^57+2781x^58+2060x^59+1483x^60+982x^61+567x^62+348x^63+129x^64+64x^65+57x^66+40x^67+10x^68+4x^69+2x^70

The gray image is a code over GF(2) with n=220, k=15 and d=92.
This code was found by Heurico 1.13 in 12.7 seconds.