The generator matrix

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

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+13x^86+24x^87+55x^88+344x^89+47x^90+6x^91+6x^92+6x^93+3x^94+2x^95+2x^96+1x^114+2x^121

The gray image is a code over GF(2) with n=712, k=9 and d=344.
This code was found by Heurico 1.16 in 0.797 seconds.