The generator matrix

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

generates a code of length 70 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+162x^62+1116x^63+2614x^64+4838x^65+7130x^66+10710x^67+13334x^68+17420x^69+16930x^70+16940x^71+13424x^72+11296x^73+6903x^74+4258x^75+2210x^76+1008x^77+397x^78+220x^79+107x^80+28x^81+11x^82+4x^83+4x^84+3x^86+2x^88+2x^89

The gray image is a code over GF(2) with n=560, k=17 and d=248.
This code was found by Heurico 1.16 in 153 seconds.