The generator matrix

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

generates a code of length 96 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+130x^86+274x^87+418x^88+584x^89+799x^90+940x^91+1015x^92+1188x^93+1248x^94+1228x^95+1193x^96+1236x^97+1200x^98+1012x^99+906x^100+832x^101+648x^102+516x^103+352x^104+222x^105+153x^106+106x^107+55x^108+20x^109+34x^110+14x^111+26x^112+12x^113+8x^114+6x^115+4x^118+2x^120+2x^121

The gray image is a code over GF(2) with n=384, k=14 and d=172.
This code was found by Heurico 1.16 in 22.5 seconds.