The generator matrix

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

generates a code of length 55 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+42x^53+125x^54+25x^56+12x^57+30x^58+6x^60+10x^61+5x^62

The gray image is a code over GF(2) with n=220, k=8 and d=106.
This code was found by Heurico 1.16 in 3.33 seconds.