The generator matrix

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

generates a code of length 62 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+286x^60+128x^61+192x^62+128x^63+287x^64+2x^92

The gray image is a code over GF(2) with n=496, k=10 and d=240.
This code was found by Heurico 1.16 in 0.141 seconds.