The generator matrix

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

generates a code of length 53 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+24x^54+5x^56+2x^60

The gray image is a code over GF(2) with n=424, k=5 and d=216.
This code was found by Heurico 1.16 in 0.079 seconds.