The generator matrix

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

generates a code of length 91 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+139x^86+482x^87+325x^88+528x^89+410x^90+498x^91+316x^92+552x^93+323x^94+246x^95+131x^96+104x^97+4x^98+2x^99+8x^100+12x^101+2x^102+4x^105+2x^107+2x^108+1x^112+2x^115+2x^118

The gray image is a code over GF(2) with n=728, k=12 and d=344.
This code was found by Heurico 1.16 in 0.953 seconds.