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

generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+164x^88+48x^90+36x^92+4x^96+3x^112

The gray image is a code over GF(2) with n=356, k=8 and d=176.
This code was found by Heurico 1.16 in 1.72 seconds.