The generator matrix

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

generates a code of length 70 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+68x^61+159x^62+238x^63+308x^64+478x^65+538x^66+582x^67+723x^68+650x^69+741x^70+788x^71+687x^72+630x^73+476x^74+344x^75+278x^76+182x^77+97x^78+86x^79+38x^80+28x^81+29x^82+10x^83+10x^84+12x^85+6x^86+2x^88+1x^90+1x^92+1x^94

The gray image is a code over GF(2) with n=280, k=13 and d=122.
This code was found by Heurico 1.16 in 4.95 seconds.