The generator matrix

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

generates a code of length 68 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+108x^61+1506x^62+2268x^63+4217x^64+5048x^65+7610x^66+7556x^67+9367x^68+7360x^69+8002x^70+4704x^71+3923x^72+1864x^73+1214x^74+428x^75+193x^76+76x^77+52x^78+20x^79+9x^80+8x^81+2x^88

The gray image is a code over GF(2) with n=544, k=16 and d=244.
This code was found by Heurico 1.16 in 35.6 seconds.