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

generates a code of length 89 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+312x^88+128x^90+64x^92+6x^96+1x^128

The gray image is a code over GF(2) with n=712, k=9 and d=352.
This code was found by Heurico 1.16 in 34.4 seconds.