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

generates a code of length 93 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+168x^89+788x^90+724x^91+520x^92+524x^93+264x^94+256x^95+216x^96+180x^97+189x^98+92x^99+60x^100+32x^101+69x^102+8x^103+1x^106+2x^108+1x^110+1x^112

The gray image is a code over GF(2) with n=744, k=12 and d=356.
This code was found by Heurico 1.16 in 0.578 seconds.