The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  X  X  2  X  X  2  X  1  0  1  X  1  1  1  1  X  1  2  1  X
 0  X  0  0  0  0  0  0  2  2  X X+2  X  0  0  2 X+2 X+2  X  X  X  0  X  X  2 X+2  X X+2  2 X+2  X  2  2  X  0  X  0  2  0  2  X  0 X+2  0  2  X  2  2  0  0  X  X  0  2 X+2
 0  0  X  0  0  0  0  0  0  0  0  0  2 X+2 X+2 X+2  X X+2 X+2  X  2 X+2  X  2  X  X  X  2  X  X  0  X  2  0  X  2  2  X X+2 X+2  X  0  0  2  2  X  2 X+2  2 X+2  0 X+2  X  0  0
 0  0  0  X  0  0  2 X+2  X  X  X  X  2 X+2  X  2  2  0  2  2  2  2  X X+2  2  X X+2  X  X X+2  2  X  X  0  X  0  X  0  X  0 X+2 X+2  2  2  2  2 X+2  2 X+2 X+2  X  X  0 X+2  0
 0  0  0  0  X  0 X+2 X+2  X  2 X+2 X+2  0  X  X  0  2  X  0 X+2 X+2 X+2  X  0 X+2 X+2  2  0  0  2  X  2 X+2  0  2 X+2  2  X  0  0 X+2  2  X  X  2  2 X+2  0  0  0  0 X+2  0  2  0
 0  0  0  0  0  X  X  2 X+2  X X+2  2  X  X  0  X  0 X+2 X+2  0  X  2 X+2  X  X  2  0  0  2  X  2 X+2  0  2  X  0  0  2  X  X  2  X X+2  0  2  0  0  0  0 X+2  X X+2 X+2 X+2  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+188x^46+395x^48+48x^49+572x^50+244x^51+860x^52+400x^53+1066x^54+636x^55+1159x^56+464x^57+804x^58+204x^59+511x^60+48x^61+338x^62+4x^63+155x^64+68x^66+20x^68+4x^70+2x^72+1x^84

The gray image is a code over GF(2) with n=220, k=13 and d=92.
This code was found by Heurico 1.16 in 4.57 seconds.