The generator matrix

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

generates a code of length 55 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+4x^54+104x^55+7x^56+4x^57+3x^58+4x^61+1x^66

The gray image is a code over GF(2) with n=440, k=7 and d=216.
This code was found by Heurico 1.16 in 0.078 seconds.