The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+118x^61+894x^62+2520x^63+4984x^64+8632x^65+14170x^66+20326x^67+27793x^68+33354x^69+36035x^70+33120x^71+28790x^72+21478x^73+13826x^74+7946x^75+4377x^76+2190x^77+1033x^78+258x^79+167x^80+88x^81+26x^82+2x^83+10x^85+2x^87+2x^89+2x^91

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 606 seconds.