The generator matrix

 1  0  1  1  1 X^2+X+2  1  1 X^2+2  1  1  2  1  1  X  1  1 X^2  1  1 X^2+X  1 X+2  1  1  1  1  1  0 X+2  1  1  1  1 X^2+2 X^2+X  1  1  1  1 X^2  X  1 X^2+X+2  1  1  1  1  1  1 X^2 X^2 X+2 X^2+X  1  1 X^2  1  1  1  1  1
 0  1 X+1 X^2+X+2 X^2+1  1  2 X^2+X+1  1 X^2+2 X+1  1  X  3  1 X^2 X^2+X+3  1 X^2+X X^2+3  1  1  1 X+2 X^2+X X^2+2 X+3  1  1  1  0 X+2 X^2+X+1 X^2+3  1  1 X+1  1  1 X+3  X X^2+X X^2+X+1  1 X^2+3  3 X^2+X+1 X^2+3 X+2 X+2  1  1  1  1  2  2  1  3 X^2+X+2 X^2+X+2 X^2+2  0
 0  0 X^2 X^2  2 X^2 X^2+2 X^2+2  2  2  0 X^2+2 X^2  2 X^2 X^2+2  0 X^2+2  0 X^2  0 X^2+2  2  0  2  0 X^2+2 X^2  2  0  2  2 X^2 X^2+2  0  2  0  0 X^2 X^2 X^2 X^2+2  2  2 X^2+2 X^2+2  2  2  2 X^2+2 X^2  0 X^2+2 X^2 X^2  0 X^2  0 X^2  2  2  0
 0  0  0  2  0  0  0  2  2  2  2  2  0  2  2  2  0  0  0  0  0  2  2  2  0  2  0  2  0  2  0  2  2  0  2  0  0  2  0  2  2  0  2  2  2  0  0  2  0  2  2  0  2  2  2  2  0  0  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+89x^58+266x^59+252x^60+368x^61+272x^62+248x^63+148x^64+228x^65+110x^66+30x^67+20x^68+12x^69+1x^74+1x^76+1x^80+1x^84

The gray image is a code over GF(2) with n=496, k=11 and d=232.
This code was found by Heurico 1.16 in 0.25 seconds.