The generator matrix

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

generates a code of length 61 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+212x^54+944x^55+2148x^56+3818x^57+5594x^58+7562x^59+8198x^60+9088x^61+8391x^62+7116x^63+5408x^64+3602x^65+1834x^66+940x^67+392x^68+172x^69+63x^70+28x^71+13x^72+8x^73+2x^74+2x^75

The gray image is a code over GF(2) with n=488, k=16 and d=216.
This code was found by Heurico 1.16 in 33.6 seconds.