The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+40x^55+2x^56+16x^57+3x^58+1x^60+1x^62

The gray image is a code over GF(2) with n=440, k=6 and d=220.
This code was found by Heurico 1.16 in 0.094 seconds.