The generator matrix

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

generates a code of length 67 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+112x^59+894x^60+2528x^61+4408x^62+7070x^63+11109x^64+14274x^65+15984x^66+17960x^67+17080x^68+14340x^69+10487x^70+7066x^71+4211x^72+1930x^73+950x^74+418x^75+144x^76+76x^77+11x^78+12x^79+1x^80+4x^85+2x^91

The gray image is a code over GF(2) with n=536, k=17 and d=236.
This code was found by Heurico 1.16 in 155 seconds.