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

generates a code of length 61 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+464x^58+144x^59+440x^60+536x^62+96x^63+228x^64+118x^66+16x^67+2x^72+1x^80+2x^82

The gray image is a code over GF(2) with n=488, k=11 and d=232.
This code was found by Heurico 1.16 in 42.1 seconds.