The generator matrix

 1  0  1  1  1  X  1  1 X^2+X  1  1  X X^2+X+2 X^2  1  1  1  1 X^2+X+2  1  1 X^2+2  1  1  1  1 X^2  1  1 X^2+2  0  1  1  1  1  1  X  0  0 X+2  1 X^2+X  1  1  1 X+2  1  1  1  1  1  1  1  1  2 X^2+X  1  1  1  1  1  1  1 X^2+2 X^2+2  1  1 X^2+2  1  2  1  1
 0  1  1 X^2 X+1  1  X  3  1 X^2+X X+3  1  1  1 X^2 X^2+1  X X+3  1  2 X^2+X+3  1 X^2+X+2  3  0 X^2+X+1  1  1 X^2+X+3  1  1  X X+1 X^2+X+2 X^2+2 X^2+X+3  1  1  1  1 X^2+3  1 X^2+3 X^2+3 X+2  1 X^2+X+2  0 X^2  3  1 X+3  0 X+3  1  1  X X+3 X^2+1 X+1 X^2+X+3  3  3  1  1 X^2+X+3 X^2  1 X+2  1 X+3  0
 0  0  X X+2  2 X+2 X+2  2  0  0  X X^2+X X^2+2 X^2 X^2+X+2 X^2+2 X^2+X+2 X^2  X X^2 X^2+X X^2+X+2 X^2 X^2+X X^2+X X^2+2  X X^2  X  2 X^2+X+2  2 X^2+X+2 X+2 X^2+2  2 X^2 X+2 X^2  2 X+2 X^2+X  0 X^2+X X^2 X^2+2 X^2+X+2  X  2  0 X^2+X+2 X^2+2 X+2 X^2+X X^2+X X+2  0  0 X^2  X X^2+X+2  X X+2 X+2 X^2+2  0 X^2+X X^2+X  X  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+72x^68+330x^69+291x^70+238x^71+242x^72+214x^73+271x^74+282x^75+76x^76+4x^77+4x^78+16x^79+4x^81+1x^88+1x^98+1x^102

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 0.281 seconds.