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

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+30x^61+207x^62+15x^64+2x^77+1x^94

The gray image is a code over GF(2) with n=496, k=8 and d=244.
This code was found by Heurico 1.16 in 13.9 seconds.