The generator matrix

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

generates a code of length 70 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+482x^66+128x^67+1085x^68+160x^69+680x^70+96x^71+846x^72+96x^73+338x^74+32x^75+80x^76+60x^78+8x^82+2x^84+1x^88+1x^92

The gray image is a code over GF(2) with n=560, k=12 and d=264.
This code was found by Heurico 1.16 in 0.516 seconds.