The generator matrix

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

generates a code of length 62 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+74x^53+514x^54+1732x^55+4775x^56+7736x^57+14081x^58+19820x^59+28984x^60+34040x^61+37669x^62+34598x^63+29783x^64+20710x^65+13995x^66+6976x^67+3840x^68+1512x^69+831x^70+226x^71+165x^72+52x^73+12x^74+8x^75+4x^76+2x^77+2x^78+2x^81

The gray image is a code over GF(2) with n=496, k=18 and d=212.
This code was found by Heurico 1.16 in 539 seconds.