The generator matrix

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

generates a code of length 86 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+29x^80+50x^81+37x^82+52x^83+48x^84+154x^85+293x^86+160x^87+42x^88+46x^89+26x^90+44x^91+24x^92+6x^93+11x^94+1x^170

The gray image is a code over GF(2) with n=344, k=10 and d=160.
This code was found by Heurico 1.16 in 0.553 seconds.