The generator matrix

 1  0  1  1  1  X  1  1 X^2+X+2  1  2  1  1  1  1 X^2+X+2  1 X^2+2  1 X^2  1  1  1 X^2+2  1  1  0 X+2  1 X^2+X  1  1  0  1 X+2  1 X^2+X+2  1  1  1 X^2+2  1 X+2 X+2  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  2  0  1  1  1 X^2+2 X^2 X+2  1  0  1
 0  1  1 X^2 X+1  1  X X^2+X+1  1  X  1 X^2+X+3 X^2+X+3 X^2+1  0  1 X^2+X+2  1 X^2+X+2  1 X^2+X+3 X^2+3 X+2  1  1 X^2+2  1  1  2  1 X^2+1 X^2+2  1 X+3  1 X^2+1  1 X^2 X^2+X+2  1  1 X+2  1  1 X+1  2  1 X^2+X+2 X+1 X^2+X+3 X+2 X+1 X+3 X^2+3 X^2+X+1 X^2+1  3  1  X X^2+X  0  1 X^2+2 X^2+X  X  1  1  1 X^2+X+3  1  1
 0  0  X X+2  2 X+2 X+2  X X^2+2 X^2 X+2 X^2+2 X^2+X+2 X^2+X X^2+2  0  0 X^2 X+2 X+2  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^2 X^2+2 X+2  0  X X^2+X  0 X^2+2  2  0  0 X^2 X^2+X X^2+X X^2+X X^2+X X^2+X X^2+2  0 X^2+X X^2  2 X^2+X X^2 X^2+X+2 X^2+2  0  2 X^2+X+2  X X^2+X X^2+2 X+2  X  2  0  2  X X^2 X+2

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+360x^68+332x^69+357x^70+176x^71+230x^72+200x^73+248x^74+48x^75+56x^76+12x^77+17x^78+8x^80+1x^86+1x^94+1x^96

The gray image is a code over GF(2) with n=568, k=11 and d=272.
This code was found by Heurico 1.16 in 0.265 seconds.