The generator matrix

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

generates a code of length 55 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+96x^50+188x^51+296x^52+220x^53+282x^54+164x^55+187x^56+172x^57+116x^58+68x^59+81x^60+52x^61+64x^62+28x^63+15x^64+4x^65+8x^66+1x^68+2x^70+3x^72

The gray image is a code over GF(2) with n=220, k=11 and d=100.
This code was found by Heurico 1.11 in 0.125 seconds.