The generator matrix

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

generates a code of length 85 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+19x^80+184x^81+78x^82+150x^83+52x^84+158x^85+35x^86+148x^87+34x^88+78x^89+11x^90+6x^91+17x^92+42x^93+3x^94+2x^96+1x^100+2x^112+2x^113+1x^122

The gray image is a code over GF(2) with n=340, k=10 and d=160.
This code was found by Heurico 1.16 in 0.504 seconds.