The generator matrix

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

generates a code of length 70 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+170x^61+899x^62+2290x^63+4857x^64+8868x^65+13978x^66+21300x^67+27341x^68+33246x^69+35227x^70+34538x^71+27992x^72+21232x^73+13573x^74+8496x^75+4534x^76+2068x^77+960x^78+308x^79+136x^80+72x^81+33x^82+8x^83+1x^84+8x^85+2x^86+4x^87+2x^88

The gray image is a code over GF(2) with n=560, k=18 and d=244.
This code was found by Heurico 1.16 in 654 seconds.