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  2  X X^2  X  0  X  X X^2+2  X  X  X  0  X X^2+2  X  X  X  0 X^2+2  X  X X^2  X  X  X X^2  X X^2 X^2
 0  X  0 X^2+X+2 X^2 X^2+X X^2+2  X  0 X^2+X+2  0 X^2+X X^2  X X^2+2  X  2 X^2+X+2  2 X^2+X  2 X^2+X+2  2 X^2+X X^2+2 X+2 X^2 X+2 X^2+2 X+2 X^2 X+2 X^2+X  X X+2  X X^2+X+2  X X^2  X  X X^2+2  2 X^2+X+2  X  X  X X^2+X+2  X  0  X  X  0 X^2+2 X^2+2 X^2+X X^2+X X^2+X  2 X^2+X+2  0  0
 0  0 X^2+2 X^2 X^2  2  2 X^2+2  2 X^2+2 X^2  0 X^2+2 X^2  0  2  2  2 X^2 X^2+2  0  0 X^2+2 X^2 X^2+2 X^2+2  2  0 X^2 X^2  0  2  0 X^2  2 X^2+2 X^2  0 X^2+2 X^2  2 X^2+2 X^2  0 X^2  2 X^2+2 X^2+2 X^2+2 X^2  2  0  0  0  2 X^2+2 X^2  2 X^2  0 X^2  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+158x^60+96x^61+88x^62+117x^64+32x^65+8x^66+6x^68+2x^72+4x^76

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.