The generator matrix

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

generates a code of length 55 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+128x^49+192x^50+438x^51+384x^52+456x^53+423x^54+436x^55+303x^56+336x^57+233x^58+282x^59+150x^60+132x^61+70x^62+72x^63+26x^64+16x^65+9x^66+4x^67+4x^69+1x^70

The gray image is a code over GF(2) with n=220, k=12 and d=98.
This code was found by Heurico 1.16 in 0.659 seconds.