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  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
 0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2  2 X^2  2 X^2  2 X^2  2 X^2  2 X^2  2 X^2  2 X^2  2 X^2  2 X^2  2  2 X^2 X^2  2 X^2  2 X^2+2  2 X^2  2  0
 0  0  2  0  0  0  2  0  0  0  0  0  2  0  2  0  0  2  0  2  0  2  0  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  2  0  2  0  0  0  2  0  0  0  2  2  0  2  0  0
 0  0  0  2  0  0  0  2  0  0  0  0  0  2  0  2  2  2  2  2  2  2  2  2  2  0  2  0  2  0  2  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  2  2  2  0  2  0  2  2  2  0  2  0  0  2  0  0
 0  0  0  0  2  0  2  0  0  2  2  2  2  2  0  2  2  0  2  0  0  2  0  2  0  2  0  2  2  0  2  0  0  0  0  2  2  2  2  2  2  2  0  0  0  2  2  2  0  0  2  2  0  0  2  0  0  0  2  0  0  0
 0  0  0  0  0  2  0  2  2  2  2  0  2  0  2  2  0  0  2  2  2  2  0  0  0  0  2  2  2  2  0  0  0  2  2  2  2  0  0  0  0  2  0  0  2  0  2  2  2  0  2  0  0  2  0  2  0  0  2  2  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+63x^60+896x^62+63x^64+1x^124

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 0.234 seconds.