The generator matrix

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

generates a code of length 70 over Z4[X]/(X^2+2X+2) 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 0.422 seconds.