The generator matrix

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

generates a code of length 67 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+188x^60+1212x^61+2314x^62+4016x^63+5748x^64+6950x^65+7873x^66+9278x^67+8149x^68+7122x^69+5102x^70+3678x^71+2072x^72+1044x^73+413x^74+186x^75+93x^76+38x^77+42x^78+10x^79+5x^80+2x^81

The gray image is a code over GF(2) with n=536, k=16 and d=240.
This code was found by Heurico 1.16 in 35.9 seconds.