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

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

Homogenous weight enumerator: w(x)=1x^0+197x^62+16x^63+331x^64+60x^65+444x^66+152x^67+396x^68+276x^69+490x^70+288x^71+375x^72+164x^73+367x^74+56x^75+162x^76+12x^77+146x^78+96x^80+45x^82+14x^84+7x^86+1x^104

The gray image is a code over GF(2) with n=280, k=12 and d=124.
This code was found by Heurico 1.16 in 46.8 seconds.