The generator matrix

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

generates a code of length 71 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+348x^61+708x^62+1302x^63+1700x^64+2754x^65+3314x^66+4058x^67+4549x^68+5370x^69+5515x^70+5890x^71+5674x^72+5710x^73+4888x^74+4314x^75+3065x^76+2470x^77+1568x^78+1118x^79+536x^80+336x^81+186x^82+80x^83+26x^84+30x^85+13x^86+6x^87+4x^89+2x^93+1x^104

The gray image is a code over GF(2) with n=284, k=16 and d=122.
This code was found by Heurico 1.13 in 67.9 seconds.