The generator matrix

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

generates a code of length 55 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+36x^53+80x^54+60x^55+14x^56+28x^57+30x^58+4x^59+1x^64+2x^66

The gray image is a code over GF(2) with n=220, k=8 and d=106.
This code was found by Heurico 1.16 in 0.0624 seconds.