The generator matrix

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

generates a code of length 55 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+4x^54+40x^55+7x^56+8x^57+2x^58+1x^66+1x^74

The gray image is a code over GF(2) with n=220, k=6 and d=108.
This code was found by Heurico 1.16 in 0.0395 seconds.