The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  X  X  X  2  1  2  0  0  2  X  1  2  1  0  1  2  1  X  1  X  0  1  0  X  2  1  1  1  1  1  X
 0  X  0  0  0  0  0  0  2  2  X X+2  X  0  0  2 X+2 X+2  X  X  X  X  0  X X+2  X  0  X X+2  2 X+2  2  2 X+2  X  0  0  X  2  2 X+2  2  X  X  2  X  X  X X+2  0  X  0  X X+2  X  2  2  2 X+2  X  X  2 X+2  X X+2 X+2  0  X X+2 X+2
 0  0  X  0  0  0  0  0  0  0  0  0  2 X+2 X+2 X+2  X X+2 X+2  X  2  2 X+2 X+2  0  0  X  X  X X+2 X+2 X+2  2  2 X+2  X  X  2  2  X  X  0  X  2  X  X X+2  0  0 X+2  0  0  X  2  X  2 X+2  2  X  X X+2  0  0  2  X  X X+2  0  0  X
 0  0  0  X  0  0  2 X+2  X  X  X  X  2 X+2  X  2  2  0  2  2  2  2  2  X X+2  X  2  X X+2 X+2  X X+2  0  2  0  0  0 X+2  2  X X+2  0  0  0  X  0  X  X  2  0 X+2  X  X  X  0 X+2  0  2 X+2 X+2  2  X  X  X  0  2  X  2  0  X
 0  0  0  0  X  0 X+2 X+2  X  2 X+2 X+2  0  X  X  0  2  X  0 X+2 X+2  X X+2  X  2  2  X  2  2  0 X+2  2  0 X+2  X X+2  2  0  X  0  0  2  0  X  0 X+2  0  X  0 X+2  2 X+2  X  2  X  X  0  2  0 X+2  X  0 X+2  X X+2 X+2  X X+2  2  0
 0  0  0  0  0  X  X  2 X+2  X X+2  2  X  X  0  X  0 X+2 X+2  0  X  2  2 X+2  2  X X+2 X+2  2  X  2  2 X+2  0  X X+2  0  0  X  X  0 X+2  2  2  2  0  X X+2 X+2  X  0 X+2  X X+2 X+2 X+2  0  X  2 X+2  X  2  0 X+2  2 X+2  2  2  0  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+131x^60+4x^61+368x^62+32x^63+590x^64+144x^65+730x^66+328x^67+935x^68+500x^69+888x^70+496x^71+810x^72+412x^73+654x^74+104x^75+467x^76+24x^77+258x^78+167x^80+4x^81+96x^82+34x^84+14x^86+1x^100

The gray image is a code over GF(2) with n=280, k=13 and d=120.
This code was found by Heurico 1.16 in 6.08 seconds.