The generator matrix

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

generates a code of length 96 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+102x^83+456x^84+914x^85+1650x^86+2320x^87+3350x^88+4314x^89+5223x^90+6116x^91+7389x^92+8856x^93+9343x^94+9840x^95+10325x^96+10516x^97+9683x^98+9092x^99+7852x^100+6372x^101+5249x^102+3862x^103+2972x^104+2012x^105+1314x^106+824x^107+553x^108+256x^109+128x^110+88x^111+28x^112+36x^113+12x^114+10x^115+2x^116+2x^117+6x^118+2x^119+2x^121

The gray image is a code over GF(2) with n=384, k=17 and d=166.
This code was found by Heurico 1.13 in 347 seconds.