The generator matrix

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

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+73x^68+336x^69+281x^70+284x^71+239x^72+232x^73+197x^74+240x^75+70x^76+54x^77+30x^78+4x^79+2x^82+1x^86+1x^90+1x^92+2x^93

The gray image is a code over GF(2) with n=576, k=11 and d=272.
This code was found by Heurico 1.16 in 0.406 seconds.