The generator matrix

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

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+218x^60+128x^61+364x^62+128x^63+146x^64+36x^66+2x^68+1x^112

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 0.281 seconds.