The generator matrix

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

generates a code of length 62 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+608x^55+2134x^56+4480x^57+6973x^58+10458x^59+14707x^60+16968x^61+18231x^62+17290x^63+14866x^64+10886x^65+6897x^66+3684x^67+1572x^68+780x^69+357x^70+114x^71+47x^72+6x^73+6x^74+6x^75+1x^84

The gray image is a code over GF(2) with n=496, k=17 and d=220.
This code was found by Heurico 1.16 in 147 seconds.