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

generates a code of length 71 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+146x^69+85x^70+136x^71+9x^72+60x^73+24x^74+40x^75+4x^76+2x^77+2x^78+1x^80+1x^86+1x^88

The gray image is a code over GF(2) with n=568, k=9 and d=276.
This code was found by Heurico 1.16 in 6.5 seconds.