The generator matrix

 1  0  0  1  1  1  2  0  1  1  2  0  1  1  1  1  1  1 X+2 X+2 X^2+X  1  X  1  X  1  X  1 X^2  1  1  1  1  1  X X^2+2 X^2+X  1  1  1  1  1  1 X+2  0 X^2+2 X^2+X  1  1  1 X^2+X+2  1  1  X X^2  1  1  1 X^2+X X^2+X+2  1 X^2
 0  1  0  0 X^2+1 X^2+1  1 X^2+X  2 X^2+3  1  1  2 X^2+3  X X^2+X+1 X+2 X^2+X+3  1 X^2+X  1 X^2+X+3 X^2 X+1  1 X^2+X+2  1 X^2+X+2  1  1  X  3  3 X^2+X+1  1  1 X^2+2 X^2+X X+1  0 X+1 X^2+3 X+3  1 X^2  1  1  1  0 X^2+X+1 X^2+X+2 X^2 X^2+X+3  1  1 X+2  0  1  1  1 X+2 X^2+X
 0  0  1 X+1 X+3  2 X^2+X+3  1 X^2+X+2 X^2+1  1 X^2+X X^2+3 X^2+X  X  2 X^2+X+3 X^2+1 X^2+X+2  1 X+1 X^2+X  1 X+3 X^2+3 X+3 X^2+2  3 X^2 X^2+X+3 X^2+X X+2  2  1 X+1 X^2+X  1 X^2+3 X^2+X+3 X+2 X^2+2  0  X  0  1 X^2+1 X^2+2  1 X+2 X^2+X+3  1 X^2+3 X^2 X+2  0 X^2+2 X+3  1  1 X^2+X+1 X^2+X+2  1
 0  0  0  2  2  0  2  2  2  0  0  2  0  2  2  0  2  0  0  0  0  2  2  2  2  0  0  2  2  0  0  0  2  2  2  0  0  0  2  2  0  2  0  0  0  2  2  0  0  0  2  2  2  2  0  0  0  2  0  2  0  0

generates a code of length 62 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+629x^58+752x^59+1446x^60+1024x^61+1361x^62+656x^63+988x^64+360x^65+455x^66+216x^67+141x^68+56x^69+83x^70+8x^71+15x^72+1x^76

The gray image is a code over GF(2) with n=496, k=13 and d=232.
This code was found by Heurico 1.16 in 55.5 seconds.