The generator matrix

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

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+454x^62+1561x^64+2272x^66+2610x^68+2878x^70+2635x^72+2006x^74+1206x^76+502x^78+170x^80+72x^82+8x^84+6x^86+1x^88+2x^90

The gray image is a code over GF(2) with n=280, k=14 and d=124.
This code was found by Heurico 1.13 in 144 seconds.