The generator matrix

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

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+139x^60+40x^61+508x^62+196x^63+782x^64+656x^65+1244x^66+964x^67+1594x^68+1252x^69+1748x^70+1212x^71+1764x^72+940x^73+1138x^74+588x^75+672x^76+244x^77+356x^78+48x^79+152x^80+4x^81+78x^82+41x^84+16x^86+5x^88+2x^92

The gray image is a code over GF(2) with n=280, k=14 and d=120.
This code was found by Heurico 1.16 in 16.6 seconds.