The generator matrix

 1  0  0  1  1  1  2  1  1  2  1  1  0 X^2  1  1  1  1 X^2+X+2  X X+2  1  1  1  1  X X^2+X+2 X+2  1 X^2  1  1  1  2 X^2+2  1  0  1 X^2+X+2 X^2+X+2  2  1  1  1  1  1 X^2+X+2  X  1  X  1  1 X^2  1  2 X^2+2  1  1 X^2+X  1  1 X^2  1  1  1 X^2+X  1  1  1  1 X+2  1
 0  1  0  2 X^2+1 X^2+3  1  0 X^2+1  1  2 X^2+3  1  X X+2  X X^2+X+3 X^2+X+1 X^2+2  1  1 X+3 X^2+X+2 X+1 X^2+X X^2+X  1  1  X X^2 X+2  3 X+3  1 X^2+X+2 X^2+X+1  1 X^2+X+1  X  1  1 X+1  1  2  0 X^2+X+2  1 X^2+2  2  1  0 X+3  1  1  1  1 X^2+X X^2+X+3  1  3  1  1 X^2+1  3 X^2 X^2+X+2 X^2 X^2+X+2 X^2 X^2+3  1  0
 0  0  1 X+3 X+1  2 X^2+X+1 X^2+X X^2+1  3 X^2+3 X^2+X+2 X^2+X+2  1 X+2 X^2+3 X+1  X  1 X^2+X+1  X  2 X+3  1 X^2  1 X+1  0  1  1 X^2+X X^2+1 X^2+2  X  1 X^2+X+1 X^2+1  3  1 X^2+1 X^2+2 X^2+X+2  X X^2 X^2+X+3  0 X^2  1  X X^2+1  3  X  3 X^2 X+1 X^2+3  3 X^2+3 X^2+X X^2+X+1  0  X  1 X^2+X+2 X^2+X+1  1 X^2+X+2 X+2  2 X^2+2 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+122x^68+694x^69+664x^70+678x^71+418x^72+428x^73+248x^74+348x^75+165x^76+138x^77+84x^78+70x^79+21x^80+12x^81+2x^82+1x^84+2x^86

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 0.297 seconds.