The generator matrix

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

generates a code of length 72 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+489x^68+360x^69+540x^70+448x^71+569x^72+368x^73+536x^74+320x^75+370x^76+40x^77+12x^78+23x^80+11x^84+5x^88+2x^92+2x^96

The gray image is a code over GF(2) with n=576, k=12 and d=272.
This code was found by Heurico 1.16 in 27.4 seconds.