The generator matrix

 1  0  0  1  1  1  2  1  1  1  1  0  2 X^2  1  1 X^2+X+2  1  1 X^2  X X^2+X+2  1  1  0  X  1  1  1 X^2+X+2  1 X+2  1 X+2  1  1  1  X X^2  1 X^2+X  1 X^2+2 X^2+X X^2+2  1  1  0  1  1  1  1  1  1  1  1  1  1 X+2 X^2+X  0  1
 0  1  0  2 X^2+1 X^2+3  1 X^2 X^2+2  1  3  1  1  X  X X+2  1 X+1 X^2+X+3 X^2+X+2  1  1 X^2+X X^2+X+2 X^2  1 X^2+1  3 X+3 X^2+2 X+1  X X^2+X+1  2 X^2+X+2 X^2+X+3  2  1  1  3  X X+2  1  1  1 X^2+2 X^2+X+2 X^2+X  1  3 X^2+X X^2+X  2 X^2+X  0 X+2 X^2+X+1 X^2+2  1  1  1  0
 0  0  1 X+3 X+1  2 X^2+X+1  X  3  1 X+2  X  3  1 X^2+X+2  3  X X^2+X+3 X+2  1 X^2+X+1 X^2+2 X^2+2 X+3  1  3 X^2+X+3 X^2+X X^2+3  1 X^2  1 X^2+X+1  1  3 X^2+X  X X^2+3 X^2+X+2 X^2+3  1 X+1 X^2+X+3  2 X^2+3 X^2+1  0  1 X^2 X+1 X^2+X+3  X X^2+2  2 X^2+X+3 X+3 X+1 X^2+X+1  0 X^2+X+2 X^2+X  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+114x^58+566x^59+644x^60+774x^61+514x^62+492x^63+301x^64+282x^65+101x^66+112x^67+84x^68+64x^69+20x^70+14x^71+10x^72+3x^74

The gray image is a code over GF(2) with n=496, k=12 and d=232.
This code was found by Heurico 1.16 in 0.219 seconds.