The generator matrix

 1  0  1  1  1  2  1  1  X  1  1 X+2  1  1  2  1  1  0  1  1  X  1  1 X+2  1  1 X+2  1  1  0  1  2  1  1  X  1  1  2  1 X+2  1  1  0  1  X  1  0  1  1  X  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  X  X  2  1  1  0  0  1  1  X  0  1  1  1  1  1  2  1  X  0  2  X  X
 0  1  1  0 X+1  1 X+3  0  1  0  3  1  0 X+3  1  0 X+1  1  0  3  1  0  1  1  X X+3  1  X  3  1 X+2  1 X+1 X+2  1  3  X  1  X  1 X+3  X  1  X  1  1  X X+3  1  0 X+3  1 X+1  1 X+1 X+1 X+1 X+1 X+1 X+1  2  3  3  3  3  3  3  1  1  X  2  2  1  1  2 X+2  2  X X+2  2  X  X X+2  X X+2  1  1  1  2  1
 0  0  X  0  0  0  0  X  X  X  X  X  2  2  2  2  2  2 X+2 X+2 X+2 X+2 X+2 X+2  X  X  0  0  2 X+2  X  X  2  0  2 X+2 X+2 X+2  2  0  0 X+2  X  2  2  X  X  2 X+2  X  X  0 X+2  0  X  X X+2 X+2  0 X+2 X+2  X  2  0  0  2  2 X+2  X X+2  0  0  2  0 X+2  X  0  0  2  2  0  2  X X+2  X  X  X  0  X  0
 0  0  0  X  2 X+2 X+2  X  2  2 X+2  X  2  0  2 X+2  X  X X+2  2 X+2  0  X  0  0  2  0 X+2 X+2 X+2  X  0  0  0 X+2  X X+2  2  2  X  2  2  X  X  2 X+2 X+2 X+2  0 X+2  0  X  2 X+2  X X+2 X+2  X  X  0  X  2  X  0  2  2  0  0  X  X  X  0  2 X+2 X+2  0  X  X  2  0  X  0  2  0 X+2  0 X+2  2  0 X+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+248x^86+222x^88+224x^90+118x^92+124x^94+40x^96+24x^98+1x^100+16x^102+1x^112+1x^116+4x^118

The gray image is a code over GF(2) with n=360, k=10 and d=172.
This code was found by Heurico 1.16 in 13.8 seconds.