The generator matrix

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

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+101x^58+272x^59+209x^60+336x^61+213x^62+336x^63+203x^64+272x^65+99x^66+2x^68+1x^70+1x^76+1x^78+1x^94

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 0.188 seconds.