The generator matrix

 1  0  1  1 X^2  1  1  1 X^2+X  1  1  0 X+2  1  1  1  1 X^2 X^2+X+2  1  1  2  1  1 X+2  X  1  1  1  1 X+2  1  2  1  1  1 X^2  1  1 X^2+X+2  1  1 X^2+2 X^2+X+2  1 X+2  1  0 X^2+X+2  1 X^2+2  1  0  2 X+2 X^2+X+2  2  1 X^2+2 X+2  0 X^2+X  1 X+2 X^2  2  1  1 X^2 X^2+X  1  1  1  X  1  1  2  1  1  1  X  1  1  1  1  1  1  1  2  1  1
 0  1  1 X^2+X  1 X^2+X+1 X^2  3  1 X+1 X^2+X+2  1  1  0 X^2+3  2  3  1  1 X+2 X^2+X+1  1 X^2+X+2 X^2+X+1  1  1 X^2 X^2+1 X^2+2  1  1 X+2  1 X+3 X+3 X^2+X  1 X+2 X^2+1  1 X^2+X+3  3  1  1  X  1  0  1  1 X^2+X+1  1 X^2  X  1  1  1  1  0  X  1  1  1 X^2+X+2  1  1  1 X^2+1  X  1  1 X^2+2  3 X^2+X+1 X^2+X+2 X^2+X  2  0  X X+3  2  1 X+3 X^2+2  3 X^2+1 X^2+X X+3 X+2  1 X+2  0
 0  0  X  0 X+2  X X+2  2  0  2 X+2 X^2+X+2 X^2 X^2+2 X^2+2 X^2+X+2 X^2+X+2 X^2+X X^2+2 X^2+X+2 X^2+X+2 X+2 X^2+2 X^2+2  0  X X^2 X^2+X X^2+X X^2 X^2+X+2  2 X^2 X^2 X+2 X^2+X X^2+X  X X+2  2  0  2  0 X^2+X  0 X^2+2  X X^2+X+2  X X^2+X X^2+2  0  2  0  2 X^2+X+2 X+2 X^2+2 X^2+2 X^2+X+2 X^2+2 X^2 X^2  X X^2  X  0  X  2 X+2  X X^2+2 X+2 X^2+X  0  2  X X^2+X X^2  X X+2 X^2+X X^2+2  0 X^2 X^2+X+2 X^2+X+2  0  2 X^2+2  2
 0  0  0  2  0  2  2  2  2  0  0  2  2  0  2  2  0  0  0  0  2  2  2  0  0  0  2  2  0  0  2  0  2  2  0  2  2  2  2  0  2  0  2  0  2  0  0  0  2  0  0  0  2  2  2  2  0  2  2  0  2  2  0  2  0  0  0  0  2  0  0  2  0  2  0  2  2  2  0  2  2  2  0  0  0  2  2  0  2  0  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+32x^86+420x^87+492x^88+676x^89+385x^90+494x^91+286x^92+414x^93+344x^94+288x^95+95x^96+84x^97+8x^98+34x^99+13x^100+6x^101+1x^102+8x^103+4x^105+5x^106+4x^107+1x^116+1x^126

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 1.14 seconds.