The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+40x^53+6x^54+8x^55+7x^56+2x^58

The gray image is a code over GF(2) with n=424, k=6 and d=212.
This code was found by Heurico 1.16 in 0.079 seconds.