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

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

Homogenous weight enumerator: w(x)=1x^0+53x^88+414x^90+35x^92+6x^96+1x^116+2x^122

The gray image is a code over GF(2) with n=720, k=9 and d=352.
This code was found by Heurico 1.16 in 0.531 seconds.