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

generates a code of length 55 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+107x^48+160x^50+301x^52+494x^54+499x^56+222x^58+117x^60+74x^62+56x^64+10x^66+5x^68+1x^72+1x^92

The gray image is a code over GF(2) with n=220, k=11 and d=96.
This code was found by Heurico 1.16 in 0.339 seconds.