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

generates a code of length 62 over Z4[X]/(X^3+2,2X) who�s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+28x^61+82x^62+6x^64+4x^66+4x^69+2x^70+1x^80

The gray image is a code over GF(2) with n=496, k=7 and d=244.
This code was found by Heurico 1.16 in 0.125 seconds.