The generator matrix

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

generates a code of length 62 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+301x^56+1204x^57+1945x^58+3138x^59+3396x^60+4498x^61+4054x^62+4776x^63+3290x^64+2904x^65+1574x^66+868x^67+438x^68+202x^69+70x^70+64x^71+27x^72+8x^73+5x^74+2x^75+2x^76+1x^80

The gray image is a code over GF(2) with n=496, k=15 and d=224.
This code was found by Heurico 1.16 in 9.33 seconds.