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

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+87x^48+4x^49+198x^50+48x^51+277x^52+92x^53+222x^54+224x^55+316x^56+92x^57+178x^58+48x^59+102x^60+4x^61+82x^62+44x^64+16x^66+4x^68+8x^70+1x^84

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 0.324 seconds.