The generator matrix

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

generates a code of length 89 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+400x^86+246x^87+343x^88+132x^89+347x^90+214x^91+318x^92+16x^93+5x^94+24x^98+1x^132+1x^136

The gray image is a code over GF(2) with n=712, k=11 and d=344.
This code was found by Heurico 1.16 in 26.8 seconds.