The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  1  X  1  1  X  X  1  1  0  1  1  0  1  1 X+2  1  1  1  1  1  2  1 X+2  1  1  1  1  2  1  2  1  1  1  1  1  0 X+2 X+2  1  1  1  2 X+2  1  1  1 X+2  1  1  1  1  1  2  1  1  1  2  1  2  1
 0  1  1  0 X+3  1 X+1 X+2  1  2  3  1  X X+3  1  1  1 X+2  1  1  X  1  0 X+1  1  1 X+2  2 X+1  3  1 X+1  1  X  1 X+3  0  1  1  1  1  0  2  2  1  1  1  1 X+3  0  1  1  1  1  2 X+2  1  3 X+2  0 X+3  3  2  0 X+1 X+2  1 X+1  0  1
 0  0  X  0 X+2  0  2  2  X X+2  0 X+2 X+2  2  0  X X+2 X+2 X+2  2  0  0  X X+2 X+2  2  0 X+2  2  0 X+2  2  2  X  X  X  0  0  X  0  2  0  0  X X+2 X+2  0  X  2  X X+2  0  2  0  X  X  2  2  X  X X+2  0  2  0  X  2  2  X  2  2
 0  0  0  X  0  0  0  2  2  2  2  0  2 X+2 X+2  X X+2 X+2  X X+2 X+2  X X+2 X+2 X+2  X  2  2 X+2  0  0  0  0  X  2 X+2  2 X+2  X X+2  2 X+2 X+2 X+2  0 X+2  2  0 X+2  X  0  0 X+2  2  0  0 X+2  0  2  0  2  0  X  2  X X+2  2  2  X  2
 0  0  0  0  2  0  0  0  2  2  0  2  2  0  0  2  2  2  2  0  0  0  2  0  0  2  2  0  2  2  0  2  2  0  0  0  2  2  2  2  2  2  2  0  0  0  2  2  0  0  2  0  2  0  2  2  0  2  2  0  2  2  0  2  2  2  2  0  2  0
 0  0  0  0  0  2  2  2  0  2  0  2  0  0  2  2  0  2  0  2  2  0  0  0  0  0  2  2  2  0  0  2  0  0  2  2  2  2  2  0  2  0  2  0  2  2  2  2  2  2  0  2  2  2  0  2  0  0  0  2  2  2  2  0  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 63.

Homogenous weight enumerator: w(x)=1x^0+76x^63+330x^64+236x^65+164x^66+344x^67+526x^68+360x^69+164x^70+396x^71+416x^72+348x^73+172x^74+192x^75+165x^76+80x^77+12x^78+16x^79+68x^80+20x^84+8x^88+1x^92+1x^96

The gray image is a code over GF(2) with n=280, k=12 and d=126.
This code was found by Heurico 1.16 in 26.9 seconds.