The generator matrix

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

generates a code of length 96 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+178x^87+1032x^88+2114x^89+4009x^90+6074x^91+8340x^92+10368x^93+12611x^94+14450x^95+13946x^96+14154x^97+12530x^98+10254x^99+8067x^100+5176x^101+3582x^102+2002x^103+1104x^104+546x^105+250x^106+162x^107+45x^108+40x^109+9x^110+12x^111+7x^112+2x^113+1x^114+2x^115+2x^116+2x^119

The gray image is a code over GF(2) with n=768, k=17 and d=348.
This code was found by Heurico 1.16 in 250 seconds.