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  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  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  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  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  2  2  2  2  0  0  2  2  0  2  2  0  0  0  0  0  0  0  0  2  2  0  2  2  0  2  2  0  2  0  2  0  2  0  2  2  0  2
 0  0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  0  2  2  0  0  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  2  2  2  2  0  0  0  2  2  0  2  2  0  0  0  0  0  0  0  0  2  2  0  2  2  0  2  2  0  2  2  0  0  2  0  2  2  2  2  2
 0  0  0  2  0  0  0  2  2  2  2  2  0  2  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  2  2  2  2  0  0  0  0  2  2  2  2  0  0  0  2  2  0  0  2  2  0  2  2  0  0  0  2  2  0  0  0  0  2  2  2  2  0  2  0  0  0  2  0  0  2  2  2  2  0  2  2  2  0  0  2
 0  0  0  0  2  0  2  2  2  0  0  0  0  2  2  2  2  0  0  0  2  2  2  2  2  2  0  0  0  0  2  2  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  2  2  0  0  0  0  2  2  0  2  2  0  2  2  0  0  0  2  2  2  2  0  0  0  0  0  0  0  2  2  2  0  2  0  2  2  0  2  2  2  2  0
 0  0  0  0  0  2  2  0  2  2  0  2  2  2  0  0  2  0  2  2  2  0  0  2  0  2  2  0  0  2  2  0  2  2  0  0  0  0  2  2  0  0  2  2  2  2  0  0  0  2  2  0  2  0  0  2  2  2  2  2  0  0  0  0  2  2  0  0  2  2  0  0  0  0  2  2  2  0  0  2  0  0  2  0  2  0  2  2  2  2

generates a code of length 90 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+53x^88+158x^90+35x^92+6x^96+1x^116+2x^122

The gray image is a code over GF(2) with n=360, k=8 and d=176.
This code was found by Heurico 1.16 in 0.412 seconds.