The generator matrix

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

generates a code of length 63 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+454x^60+128x^61+472x^62+508x^64+128x^65+232x^66+120x^68+3x^80+2x^84

The gray image is a code over GF(2) with n=504, k=11 and d=240.
This code was found by Heurico 1.16 in 1.81 seconds.