The generator matrix

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

generates a code of length 75 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+212x^67+1178x^68+3166x^69+5333x^70+7176x^71+10801x^72+13086x^73+16439x^74+16696x^75+16125x^76+13538x^77+11037x^78+7010x^79+4679x^80+2378x^81+1152x^82+616x^83+259x^84+104x^85+48x^86+18x^87+13x^88+7x^90

The gray image is a code over GF(2) with n=600, k=17 and d=268.
This code was found by Heurico 1.16 in 182 seconds.