The generator matrix

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

generates a code of length 70 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+18x^64+144x^65+352x^66+342x^67+442x^68+496x^69+586x^70+486x^71+447x^72+296x^73+260x^74+122x^75+49x^76+24x^77+16x^78+10x^79+1x^80+1x^92+2x^94+1x^104

The gray image is a code over GF(2) with n=560, k=12 and d=256.
This code was found by Heurico 1.16 in 0.438 seconds.