The generator matrix

 1  0  0  1  1  1  2  0  1  1  2  0  1  1  1  1  1  1  X X+2 X^2+X  1  1  1 X+2  1  X X+2  2 X^2  1  1  1  1 X^2+X  1  X X^2+X+2  1  1 X^2  1  1  1 X+2  1  X  1  0  1 X^2 X+2  1  1  X  1  1 X^2  1 X^2+X  2  1 X^2+X+2 X+2 X^2+X+2  0 X^2  1  1  0 X^2+2 X^2  1  2  1  1  1  1  0 X^2+X X^2+2  1  1 X^2+2  2  X  1  1  1 X+2 X^2+2 X^2+X+2  0  1  1  1
 0  1  0  0 X^2+1 X^2+1  1 X^2+X  2 X^2+3  1  1  2 X^2+3  X X^2+X+1 X+2 X^2+X+3  1  X  1 X^2+X+1 X+2 X^2+X  1 X+1  1 X^2+X  1  1 X^2+2 X^2 X^2+X+2 X+1  X X^2+1 X^2+2  1  X  1  1 X^2+1 X^2+2  3  1 X+2  1 X^2+X+1 X^2+X X^2  1  1 X^2+X+2 X^2+3  1 X^2+X  2 X^2+X+2 X+3  1  1 X+2  2  1  1  1  2 X+1 X+2  1  1  1 X^2+X+3 X^2  2  2 X^2+X X^2+2 X+2  1  1  X  X  1  1  1 X^2+X+2 X^2+X+3 X^2+X+3  1  1  1 X^2  2 X^2+X+3  2
 0  0  1 X+1 X+3  2 X^2+X+3  1 X^2+X+2 X^2+1  1 X^2+X X^2+3 X^2+X  X X+2 X^2+X+3 X^2+X+1  1  1  X  2 X^2+2 X^2+3 X^2+X+3 X^2+3 X^2+2  1 X+3  X  3  2 X+2  1  1 X^2+X  1  1 X+3 X^2+X+1 X^2+3 X^2+3 X+1 X^2  X  1 X+1 X^2+X  1 X^2+X+2 X^2+2  2  2 X^2+X+1 X^2+X X+1 X+2  1 X^2+X+3 X+3 X^2+3 X^2+1  1 X^2+2 X^2+1 X^2+X+3  1  0 X^2+X+2 X^2  3 X+3  1  1 X^2+X+3 X^2+X+3  2 X^2+1  1 X^2+2 X^2+X+3 X+1 X^2+X+3 X^2+X+2 X^2+1  3 X^2+X+1 X+3 X+3 X+3 X^2+X+1 X^2+1  1  2 X^2+3 X^2+2
 0  0  0  2  2  0  2  2  2  0  0  2  0  2  2  2  2  2  0  0  2  0  0  0  2  2  2  2  0  0  2  2  0  0  0  0  2  2  0  0  2  2  0  2  0  2  0  2  0  0  2  2  2  2  2  2  2  2  0  0  2  2  0  0  2  0  2  2  2  2  0  2  0  0  0  2  0  0  2  0  2  2  0  0  0  2  0  0  2  2  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 91.

Homogenous weight enumerator: w(x)=1x^0+220x^91+744x^92+1156x^93+1113x^94+988x^95+856x^96+804x^97+530x^98+488x^99+294x^100+396x^101+269x^102+140x^103+109x^104+12x^105+40x^106+20x^107+10x^108+2x^124

The gray image is a code over GF(2) with n=768, k=13 and d=364.
This code was found by Heurico 1.16 in 1.52 seconds.