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

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+65x^86+146x^88+123x^90+96x^92+65x^94+10x^96+1x^98+2x^102+2x^104+1x^160

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 0.566 seconds.