The generator matrix

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

generates a code of length 62 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+350x^59+337x^60+344x^61+172x^62+280x^63+189x^64+244x^65+42x^66+38x^67+25x^68+20x^69+4x^75+2x^82

The gray image is a code over GF(2) with n=496, k=11 and d=236.
This code was found by Heurico 1.16 in 0.204 seconds.