The generator matrix

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

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+301x^60+740x^61+1268x^62+1776x^63+2651x^64+3252x^65+3990x^66+4556x^67+5159x^68+5908x^69+5878x^70+6144x^71+5476x^72+4804x^73+4108x^74+3308x^75+2465x^76+1548x^77+992x^78+568x^79+302x^80+128x^81+130x^82+32x^83+27x^84+4x^85+14x^86+2x^88+4x^90

The gray image is a code over GF(2) with n=280, k=16 and d=120.
This code was found by Heurico 1.13 in 66.2 seconds.