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  X  0  X X^2+2  X  0  X X^2+2  X  0  X X^2+2  X  2  X X^2  X  0  X  2  X X^2  X X^2  X  2  X X^2  X  X
 0  X X^2+2 X^2+X  0 X^2+X X^2+2 X+2  0 X^2+X X^2+2 X+2  0 X^2+X X^2+2  X  2 X^2+X+2 X^2  X  2 X^2+X+2 X^2 X+2  2 X^2+X+2 X^2  X  2 X^2+X+2 X^2 X+2 X^2+X  X X+2  X X^2+X  X X+2  X X^2+X  X X+2  X X^2+X+2  X  X  X X^2+X  X X^2+X+2  X  X  X  X  X X^2+X+2  X X+2  X X^2+X+2  0
 0  0  2  0  0  2  2  2  2  0  0  2  2  2  0  0  2  2  2  2  0  0  0  0  2  2  2  2  0  0  0  0  0  0  2  2  0  0  2  2  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  2  0  0
 0  0  0  2  2  2  2  0  2  0  0  2  0  0  2  2  0  0  2  2  2  2  0  0  2  2  0  0  0  0  2  2  0  2  2  0  2  0  0  2  2  0  0  2  0  2  2  0  0  2  2  0  2  0  0  2  2  0  2  2  0  0

generates a code of length 62 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+16x^60+160x^61+156x^62+160x^63+15x^64+2x^66+2x^90

The gray image is a code over GF(2) with n=496, k=9 and d=240.
This code was found by Heurico 1.16 in 0.203 seconds.