The generator matrix

 1  0  0  1  1  1  2  1  1 X+2  1  1  0  2  0  X  1  1  X X+2  1  1  1  1  1  X  1  0  1  1 X+2  1  1 X+2  1  0  2 X+2  1  1  1 X+2  1  X  X  1  1  1  0  1  0  1  1  1  2  1  1  1  1  0  X  1  1  1  1  1  1  1  1 X+2  X  1  1  1  2  2  1  1  1  1  2  X  2 X+2  X  1  1  1  1
 0  1  0  2  3  1  1  0  2  0  3  1  1  1 X+2  X  X X+1  1  1 X+2 X+3 X+2 X+3  0  1  3  1  X X+3  1  X X+1  1 X+2  2  1  2  2  1  2  1 X+1 X+2  1  3 X+3 X+2  1  0  X  1  X X+3  X  2  1  X  1  1  1  3 X+2  2 X+1 X+1  1 X+2  2  1  2  1  3 X+1  1  X  X  0  X  0  1  1  1  1  1 X+3 X+3 X+3  2
 0  0  1 X+3 X+1  2 X+1 X+2  1  1  3  X X+2  3  1  1  X X+1  3  X X+3  0  0  1 X+3  0  2  3  1  X X+1 X+1  2  1  1  1 X+3  1  X  3  0 X+2  3  1 X+1 X+2 X+3 X+2  X  3  1 X+1  0 X+2 X+2  2 X+3  2  1  2  2  0  3 X+1  X  0 X+2 X+1  3  2  1  0  X X+2  2  1  3 X+1 X+3  1  X  X  0 X+3 X+2  2  3 X+1  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+30x^86+132x^87+68x^88+104x^89+42x^90+76x^91+33x^92+4x^93+2x^94+8x^96+4x^97+4x^98+1x^100+1x^102+1x^110+1x^112

The gray image is a code over GF(2) with n=356, k=9 and d=172.
This code was found by Heurico 1.13 in 0.234 seconds.