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

generates a code of length 90 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+54x^86+38x^88+346x^90+16x^92+42x^94+8x^96+6x^98+1x^176

The gray image is a code over GF(2) with n=360, k=9 and d=172.
This code was found by Heurico 1.16 in 0.876 seconds.