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

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

Homogenous weight enumerator: w(x)=1x^0+34x^70+8x^71+10x^72+8x^73+2x^74+1x^80

The gray image is a code over GF(2) with n=280, k=6 and d=140.
This code was found by Heurico 1.16 in 0.2 seconds.