The generator matrix

 1  0  1  1 X^2  1  1  1 X^2+X  1  1  0 X+2  1  1  1  1 X^2 X^2+X+2  1  1  X  1  1  X  1  1 X^2  2  1  X  1  0  1 X^2+X+2  1  1  1 X^2+X  0  1  0  1  1  1  1 X^2+X+2  X  1  1 X^2+2  1  1  1  1  1  1 X^2+X+2 X^2 X^2+2  2 X^2+X+2
 0  1  1 X^2+X  1 X^2+X+1 X^2  3  1 X+1 X^2+X+2  1  1  0 X^2+3  2  3  1  1 X^2+3 X^2+X+1  1 X^2+2  X  1  X X+1  1  1 X^2+X  1 X+3  1 X^2+X+1  1  X X^2+1 X^2+X+3  1  1 X^2+X  1  1 X^2 X^2+X+1 X^2  1  1 X^2+X+2  2  1 X^2+3  1 X^2+X+1 X^2+3  2 X^2+1  1  1  1 X^2  1
 0  0  X  0 X+2  X X+2  2  0  2 X+2 X^2+X+2 X^2 X^2+2 X^2+2 X^2+X+2 X^2+X+2 X^2+X X^2+2  X X^2+2  X  0 X^2+X+2  0 X^2+2 X^2+X+2  X X^2+2 X^2+X+2 X^2+X X^2+2  2 X^2+X+2  X  2  0  2 X^2+X+2 X^2+X+2 X^2+2 X^2+2 X^2 X+2  X X^2  X X^2 X+2 X^2+X  2  X X^2+X+2 X+2 X^2+X X^2  0 X^2+X+2 X^2+2 X^2+X+2  X X^2+X
 0  0  0  2  0  2  2  2  2  0  0  2  2  0  2  2  0  0  0  2  0  2  2  0  0  2  2  2  2  2  0  2  2  0  2  0  0  2  2  0  0  0  0  0  0  2  0  0  2  0  2  0  2  0  2  2  2  0  2  2  2  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+310x^58+402x^59+730x^60+416x^61+566x^62+372x^63+644x^64+264x^65+250x^66+58x^67+36x^68+24x^69+4x^70+12x^72+5x^74+1x^82+1x^88

The gray image is a code over GF(2) with n=496, k=12 and d=232.
This code was found by Heurico 1.16 in 0.39 seconds.