The generator matrix

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

generates a code of length 62 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+426x^57+1050x^58+1658x^59+2378x^60+1920x^61+2385x^62+1728x^63+1861x^64+1168x^65+910x^66+452x^67+191x^68+154x^69+33x^70+32x^71+16x^72+10x^73+6x^74+2x^75+1x^76+2x^77

The gray image is a code over GF(2) with n=496, k=14 and d=228.
This code was found by Heurico 1.16 in 49.7 seconds.