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

generates a code of length 90 over Z4[X]/(X^2+2,2X) who�s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+24x^87+159x^88+48x^89+112x^90+32x^91+72x^92+16x^93+16x^94+8x^95+19x^96+4x^104+1x^120

The gray image is a code over GF(2) with n=360, k=9 and d=174.
This code was found by Heurico 1.13 in 0.235 seconds.