The generator matrix

 1  0  0  1  1  1  2  1  1  2  1  1  0  0  1  1  1  1  X X^2+X+2  2  0  1  1  1  1 X^2+X X+2  0 X^2  1 X^2+X+2 X+2 X^2+2  1  X  1  1  1  1  1 X^2 X^2+X+2 X^2 X^2+X  1  1  1 X^2  1 X^2+2  X X+2 X^2+X+2  1  1  1  1  1 X^2+X+2 X^2+X+2 X+2
 0  1  0  2 X^2+1 X^2+3  1  0 X^2+1  1  2 X^2+3  1 X^2+X X+2  X X^2+X+3 X^2+X+1 X^2+X+2 X^2+2  1  1  X X+2 X^2+X+1 X^2+X+3  X X^2 X^2+2  1 X^2+X+2  1  1  1 X^2+X+2  1 X+1 X^2+1 X^2+3 X+3 X^2+X+2  1  1 X^2+X  1 X+1  2 X^2+1  1 X^2  1  1  1  X X^2+X+2  3  3 X+3 X^2+X+1  1 X^2+X  1
 0  0  1 X+3 X+1  2 X^2+X+1 X^2+X X^2+1  3 X^2+3 X^2+X+2 X^2+X+2  1 X^2+X X^2+3 X+1  2  1  1 X^2+3 X+2 X^2+X+1 X^2+2  X  3  1  1  1  X  1  0 X^2+X+1 X^2+2 X^2+X+2  3 X^2+X+2  3 X^2+X+1 X^2  0 X^2+X+2  X  1  1 X^2+1  X X+2  0 X^2+2 X^2+X+3 X^2+2  X  1  X X+1  X  X X^2+X+1 X^2  1 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+690x^59+680x^60+744x^61+583x^62+396x^63+277x^64+236x^65+142x^66+214x^67+41x^68+76x^69+1x^70+12x^71+1x^74+1x^76+1x^82

The gray image is a code over GF(2) with n=496, k=12 and d=236.
This code was found by Heurico 1.16 in 6.2 seconds.