The generator matrix

 1  0  0  1  1  1 X+2  1  2  1  1  X  1  2  1 X+2  1  1 X+2  1  0 X+2  1  1  X  1  X  1  2  1  1  1  1  1  X  2  1  X  X  1  0  1  1  2  1  0  1 X+2 X+2  2  1  1  1  1  1  1 X+2  0  1  2  1 X+2  1  1  1  1  0  1  1  1 X+2  1  1  2  1  2  1  1  1 X+2 X+2  1  1  2  1 X+2  1  1 X+2  1  1  1  1  0  X  1
 0  1  0  0  1 X+3  1  3  1  X X+1  1  X  2  X  1 X+3 X+2  1  1 X+2  1  X  3  1  0  X X+3  1  2  0 X+1  3  2  0  1  0  1  X  0  2  X  3  1 X+3  1  3 X+2  1  1 X+1 X+2  X  1 X+1 X+2  1  X X+2  1  3  1  2 X+3  1 X+3  1  3  1  X  1 X+3  X  1  1  1 X+2 X+3  3  1  1  0  X  0  3  1  3  X  1  0  2  3  X  1 X+2  0
 0  0  1  1  1  0  1  X X+1 X+3  1 X+2  X  1 X+3  3  3 X+2  2  X  1 X+2  1 X+1 X+1  2  1  X  X X+2 X+1 X+3  2  2  1 X+1 X+3  3  1 X+3  1  0 X+2 X+3  3 X+2  3  1 X+3  0 X+3 X+2  1 X+2 X+3  2  1  1 X+3  2  2  X  1 X+2 X+1 X+1  0  X X+1  X  2  3  1  3 X+3  X  1 X+3  3  2  2  3  3  1  X X+3  2 X+1  3  0 X+3  0  0 X+1  2  2
 0  0  0  X  0  0  2  0  2  X  2  2  0 X+2  0  X X+2 X+2 X+2  X  2 X+2  0 X+2 X+2  X  X  X X+2  X  X  0 X+2  0  0  X X+2  2 X+2  2 X+2  X X+2  2  0  0 X+2  0  X  2  0 X+2  X  0  2  0 X+2  X  X  0  X  2  X  0 X+2  X X+2  X  0  X X+2  2  2 X+2  0  2  X X+2  X  0  2 X+2  X  X  2  0  X  0  X  0  X  2  2  2 X+2  X
 0  0  0  0  X X+2 X+2 X+2  X  0  X  2  2  0  0 X+2  X  2  0 X+2  0  0  2  X  X  2  2 X+2 X+2  2  0  2  0  X  X  0 X+2  2 X+2  X  X  X  0  2  0  X  2 X+2  0  X X+2 X+2 X+2 X+2  0 X+2 X+2 X+2 X+2  2  X  X  X  0 X+2  X  X X+2  0  2  2  0  0  2 X+2  0  0  X  2  0  0  2  2  2  2  X  2 X+2  0  0  X  2 X+2  0  X X+2
 0  0  0  0  0  2  0  0  2  2  2  2  2  0  2  0  2  0  2  2  2  0  0  0  2  2  2  0  0  0  2  2  0  2  0  2  2  0  0  2  2  2  2  2  0  2  2  2  0  0  0  0  2  2  0  2  2  0  2  2  2  0  0  2  0  0  0  0  0  0  0  0  2  2  2  0  0  2  0  2  0  0  2  0  0  0  0  0  0  2  0  2  0  0  0  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+87x^86+270x^87+536x^88+548x^89+801x^90+868x^91+1213x^92+988x^93+1444x^94+1064x^95+1351x^96+984x^97+1300x^98+886x^99+1065x^100+678x^101+715x^102+482x^103+410x^104+214x^105+165x^106+120x^107+77x^108+30x^109+26x^110+16x^111+14x^112+14x^113+6x^114+6x^115+5x^116

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 21.5 seconds.