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

generates a code of length 89 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+178x^85+762x^86+584x^87+677x^88+442x^89+436x^90+184x^91+200x^92+204x^93+190x^94+68x^95+89x^96+36x^97+42x^98+1x^108+1x^110+1x^114

The gray image is a code over GF(2) with n=712, k=12 and d=340.
This code was found by Heurico 1.16 in 0.5 seconds.