The generator matrix

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

generates a code of length 71 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+24x^68+90x^69+72x^70+654x^71+69x^72+86x^73+23x^74+2x^75+2x^76+1x^138

The gray image is a code over GF(2) with n=568, k=10 and d=272.
This code was found by Heurico 1.16 in 0.484 seconds.