The generator matrix

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

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+40x^85+286x^86+352x^87+380x^88+240x^89+252x^90+140x^91+119x^92+84x^93+74x^94+36x^95+33x^96+4x^97+4x^98+1x^100+2x^124

The gray image is a code over GF(2) with n=712, k=11 and d=340.
This code was found by Heurico 1.16 in 0.563 seconds.