The generator matrix

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

generates a code of length 96 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+120x^86+920x^87+2373x^88+4214x^89+7525x^90+10560x^91+16514x^92+19246x^93+26901x^94+26834x^95+31115x^96+27284x^97+28058x^98+19924x^99+15679x^100+9960x^101+7353x^102+3608x^103+2015x^104+1040x^105+477x^106+238x^107+75x^108+56x^109+20x^110+10x^111+2x^112+6x^113+6x^114+2x^115+2x^116+2x^117+4x^118

The gray image is a code over GF(2) with n=768, k=18 and d=344.
This code was found by Heurico 1.16 in 847 seconds.