The generator matrix

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

generates a code of length 55 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+64x^52+140x^53+89x^54+44x^55+52x^56+24x^57+17x^58+28x^59+12x^60+20x^61+13x^62+6x^64+1x^66+1x^72

The gray image is a code over GF(2) with n=220, k=9 and d=104.
This code was found by Heurico 1.16 in 0.049 seconds.