The generator matrix

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

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+119x^86+212x^87+486x^88+620x^89+859x^90+928x^91+997x^92+1104x^93+1142x^94+1232x^95+1317x^96+1316x^97+1041x^98+1172x^99+867x^100+812x^101+667x^102+456x^103+333x^104+224x^105+200x^106+92x^107+61x^108+20x^109+46x^110+4x^111+22x^112+19x^114+11x^116+2x^118+1x^120+1x^122

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 22.4 seconds.