The generator matrix

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

generates a code of length 96 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+30x^85+69x^86+118x^87+223x^88+228x^89+401x^90+418x^91+525x^92+606x^93+593x^94+644x^95+573x^96+648x^97+553x^98+604x^99+542x^100+442x^101+353x^102+230x^103+144x^104+84x^105+49x^106+34x^107+18x^108+10x^109+8x^110+8x^112+11x^114+10x^116+8x^118+2x^120+2x^122+1x^124+1x^126+1x^136

The gray image is a code over GF(2) with n=384, k=13 and d=170.
This code was found by Heurico 1.16 in 15.1 seconds.