The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+36x^53+8x^54+176x^55+14x^56+8x^57+6x^58+1x^64+2x^66+4x^69

The gray image is a code over GF(2) with n=440, k=8 and d=212.
This code was found by Heurico 1.16 in 0.375 seconds.