The generator matrix

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

generates a code of length 70 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+141x^60+40x^61+440x^62+272x^63+850x^64+536x^65+1202x^66+936x^67+1674x^68+1196x^69+1874x^70+1392x^71+1560x^72+964x^73+1066x^74+552x^75+779x^76+204x^77+382x^78+48x^79+135x^80+4x^81+84x^82+36x^84+8x^86+6x^88+2x^92

The gray image is a code over GF(2) with n=280, k=14 and d=120.
This code was found by Heurico 1.16 in 17 seconds.