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

generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+208x^87+60x^88+32x^89+60x^90+112x^91+32x^95+1x^96+4x^98+2x^112

The gray image is a code over GF(2) with n=356, k=9 and d=174.
This code was found by Heurico 1.16 in 55.1 seconds.