The generator matrix

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

generates a code of length 91 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+166x^87+752x^88+654x^89+624x^90+430x^91+488x^92+198x^93+198x^94+124x^95+180x^96+92x^97+88x^98+56x^99+32x^100+8x^101+1x^102+2x^108+1x^110+1x^112

The gray image is a code over GF(2) with n=728, k=12 and d=348.
This code was found by Heurico 1.16 in 0.547 seconds.