The generator matrix

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

generates a code of length 71 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+158x^67+606x^68+586x^69+822x^70+484x^71+383x^72+240x^73+338x^74+150x^75+128x^76+82x^77+78x^78+24x^79+8x^80+4x^81+2x^82+2x^88

The gray image is a code over GF(2) with n=568, k=12 and d=268.
This code was found by Heurico 1.16 in 0.297 seconds.