The generator matrix

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

generates a code of length 63 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+164x^59+85x^60+294x^61+313x^62+446x^63+288x^64+200x^65+62x^66+124x^67+9x^68+34x^69+9x^70+18x^71+1x^112

The gray image is a code over GF(2) with n=504, k=11 and d=236.
This code was found by Heurico 1.16 in 0.281 seconds.