The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  0  1  1  X X^2+2  1  1  1  X  2  1  X X^2  1  X  X  X  X  1  1  1  1  1  1  1  1  X  0  X X^2+2  X  X  2 X^2 X^2 X^2  0  2  X  X  1  1  1  1
 0  X X^2+2 X^2+X  2 X^2+X+2 X^2 X+2  0 X^2+X X^2+2 X+2  2 X^2+X+2 X^2  X X^2+X  0  X X^2+X X^2+2 X+2  X X+2  2 X^2+X+2 X^2+X+2  X X^2  X  X  X  0 X^2+2  2 X^2  0 X^2+X X^2+2 X+2  2 X^2 X^2+X+2  X X^2+X  X X+2  X X^2+X+2  X  X  X X^2+2 X^2 X^2 X^2  0  2 X^2+X X^2+X+2  0  2

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

Homogenous weight enumerator: w(x)=1x^0+114x^62+4x^64+4x^66+2x^68+2x^70+1x^72

The gray image is a code over GF(2) with n=496, k=7 and d=248.
This code was found by Heurico 1.16 in 0.125 seconds.