The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+26x^86+52x^87+102x^88+168x^89+96x^90+24x^91+24x^92+8x^93+4x^94+4x^95+2x^110+1x^128

The gray image is a code over GF(2) with n=356, k=9 and d=172.
This code was found by Heurico 1.16 in 0.532 seconds.