The generator matrix

 1  0  0  1  1  1  2  1  1  1 X+2 X^2+X  1 X^2+X+2  1  1  X  1  1 X^2+2  1 X+2  1  1  1 X^2 X^2+X  2 X^2+2  1  1 X^2+2  1  1 X^2+X  0 X^2+X  1  1  1  1  1 X^2  X  1  1  1  1  1 X+2 X^2 X^2+X+2  1  X  1  1  1  2 X^2+2 X^2+X+2 X^2+X+2  1  1  1  1  1  1  1 X^2+X  1  1  1
 0  1  0  0 X^2+1 X^2+3  1  X X^2+X+1 X^2+X+3  2  1 X^2  1 X^2+2  3  1 X^2+X X^2+3  X  X  1 X^2+X+1 X+1 X+2  1 X^2+X+2  1  1  3  0  1 X+2  X  1 X^2+2  1 X^2+X+1  0 X^2+X+3  1 X+2  1  1 X^2  2 X^2+X+3 X^2+X X+2  1 X^2+X X^2+X+2 X+1  1  1 X^2+X+1 X^2+1  1 X^2+2  2  1  2 X^2+X X^2+X+2 X^2+2  2 X^2+X X^2  1  1  0 X^2
 0  0  1 X+1 X+3 X^2 X+3  X  3  2  1 X+1  1  2 X^2+X  X  3 X^2+X+3 X^2+3  1 X^2+2  X X+2 X^2+X+1 X^2+X+3 X^2+X+3  1 X^2+3  0 X^2+2 X^2+1 X^2+X  0 X^2+1 X^2+3  1 X^2+X+1 X+1 X^2+X X^2+3  X  3 X+3  0 X+1  0 X^2  2 X^2+X X+2  1  1 X^2+X+2 X^2+2 X^2+3 X^2+X+1 X+3 X^2+1  1  1  3 X^2+X+3 X+2 X+3  1 X+3  X X+2 X^2+3 X^2+X X^2 X^2
 0  0  0  2  2  2  0  2  0  0  2  2  0  2  2  0  0  0  0  0  0  2  2  2  2  2  0  0  2  0  2  0  0  0  2  2  0  0  0  2  2  2  2  0  2  2  2  2  0  0  2  2  0  2  2  2  0  2  0  2  0  0  0  0  2  0  2  2  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+96x^67+674x^68+972x^69+1177x^70+998x^71+1123x^72+882x^73+712x^74+422x^75+406x^76+326x^77+276x^78+60x^79+35x^80+12x^81+9x^82+8x^83+1x^86+1x^88+1x^90

The gray image is a code over GF(2) with n=576, k=13 and d=268.
This code was found by Heurico 1.16 in 0.86 seconds.