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

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+141x^60+4x^61+389x^62+36x^63+551x^64+144x^65+700x^66+360x^67+882x^68+464x^69+989x^70+488x^71+848x^72+384x^73+629x^74+136x^75+466x^76+28x^77+241x^78+4x^79+147x^80+115x^82+34x^84+8x^86+1x^88+1x^94+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 6.58 seconds.