The generator matrix

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

generates a code of length 72 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+152x^67+223x^68+478x^69+447x^70+542x^71+477x^72+566x^73+415x^74+420x^75+204x^76+98x^77+17x^78+34x^79+5x^80+2x^81+1x^82+4x^83+4x^85+4x^89+1x^100+1x^104

The gray image is a code over GF(2) with n=576, k=12 and d=268.
This code was found by Heurico 1.16 in 0.578 seconds.