The generator matrix

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

generates a code of length 70 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+304x^59+821x^60+1492x^61+2383x^62+3352x^63+4534x^64+6182x^65+7947x^66+9502x^67+10747x^68+11766x^69+12297x^70+12000x^71+11263x^72+9804x^73+8079x^74+6344x^75+4522x^76+3146x^77+2050x^78+1088x^79+692x^80+412x^81+138x^82+114x^83+58x^84+28x^85+2x^86+2x^88+2x^89

The gray image is a code over GF(2) with n=280, k=17 and d=118.
This code was found by Heurico 1.13 in 242 seconds.