The generator matrix

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

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+324x^67+80x^68+364x^69+374x^70+404x^71+1153x^72+356x^73+356x^74+268x^75+71x^76+212x^77+6x^78+92x^79+5x^80+28x^81+1x^84+1x^128

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 63.9 seconds.