The generator matrix

 1  0  1  1 X^2  1  1  1 X^2+X  1  1  0 X+2  1  1  1  1 X^2  2  1  1  1  1  1  2  1 X+2  1  1  1  1 X^2+X+2  1 X^2+X  1  1  1 X^2+X  1 X+2  1  1  1  1  1 X^2+X+2  0 X^2+X+2  0  1  1  X  1  1  1  1  1  1 X^2+X+2 X+2  1 X^2  1  1 X^2+2  1  X  0  1  1 X^2  1
 0  1  1 X^2+X  1 X^2+X+1 X^2  3  1 X+1 X^2+X+2  1  1  0 X^2+3  2  3  1  1 X^2+X X+1  X X+1 X^2+2  1  1  1 X^2  2 X^2+1  3  1 X^2+X+3  1 X+2 X^2+X+1  2  1 X+3  1 X+1  X X^2+1  X X^2+X+2  1  1  1  1 X^2+X+3 X^2+X+2 X^2+X+2  1  X X^2  X X^2+1 X^2+3  1  1  X  1  3  3  1 X^2+X+1 X^2+2  X  1 X^2+X+2  1  1
 0  0  X  0 X+2  X X+2  2  0  2 X+2 X^2+X+2 X^2 X^2+2 X^2+2 X^2+X+2 X^2+X+2 X^2+X X+2 X^2+X X^2 X^2 X^2+X X^2+X X^2+2 X^2 X^2+X+2 X^2 X+2  2  X X^2+2 X^2+2 X^2+X+2 X^2+X+2  X  0  X X^2+2  0 X^2+X+2 X^2+2 X^2+X+2 X+2  2 X+2 X^2+2  2  0  0 X^2 X^2+X  2 X^2+X X+2  X X+2 X^2 X^2+X+2 X^2+2  0  X X^2+2 X^2+X X^2 X^2+X X^2+X+2 X^2+X+2 X^2+2  X  0 X^2+2
 0  0  0  2  0  2  2  2  2  0  0  2  2  0  2  2  0  0  2  0  0  2  2  0  0  0  2  2  0  0  2  0  0  0  0  0  2  2  2  2  0  0  2  2  0  0  2  0  2  2  0  0  0  2  0  0  2  0  2  0  2  2  0  2  0  0  0  2  2  2  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+382x^68+458x^69+567x^70+512x^71+586x^72+424x^73+412x^74+300x^75+204x^76+70x^77+105x^78+20x^79+22x^80+8x^81+18x^82+4x^84+1x^88+2x^94

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 0.672 seconds.