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  1  1  X  X  X  X  X  X  X  X  X  X  X  X  X  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1
 0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  2 X^2  2 X^2  2 X^2  2 X^2  2 X^2  2 X^2  2 X^2  2 X^2 X^2+2 X^2+2 X^2+2 X^2+2 X^2+2 X^2+2 X^2+2 X^2+2  0  2  0  2  0  2  0  2  0  0  0  0  2  2 X^2 X^2  2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2+2 X^2 X^2+2 X^2  2  2 X^2+2 X^2 X^2+2 X^2  2  0  0  2  2  2 X^2+2 X^2+2  0  0  0 X^2+2  2
 0  0  2  0  0  0  2  0  0  2  0  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  0  0  0  0  2  2  2  2  0  0  2  2  2  2  2  2  0  0  0  2  2  0  0  0  2  2  0  0  0  0  2  2  2  2  2  2  0  0  0  0  0  0  0  0  2  2  0  2  2
 0  0  0  2  0  0  0  2  2  2  2  2  2  0  2  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  0  0  2  2  2  2  0  0  0  0  2  2  2  2  0  0  0  2  2  0  0  2  0  2  2  2  0  0  2  2  0  2  2  0  0  0  0  0  0  2  2  2  0  0  2  0  2  2  0  0  2  2  2  0  0  2  0
 0  0  0  0  2  2  2  2  2  0  0  2  0  2  2  0  0  0  2  2  2  2  0  0  0  0  2  2  2  2  0  0  0  2  2  0  0  2  2  0  2  2  2  2  0  0  0  0  0  0  2  2  2  2  0  0  0  2  2  2  2  0  0  0  2  2  0  0  2  2  2  2  0  0  2  2  0  2  2  2  2  0  2  0  0  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+4x^86+20x^87+37x^88+412x^89+8x^90+12x^91+7x^92+4x^93+4x^94+1x^116+2x^120

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 0.813 seconds.