The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  1  X  1  1  0  1  1 X+2  1  1  2  1  1  X  1  1  0  1  1 X+2  1  1  2  1  1  X  1  1  0  1  1 X+2  1  1  1  1  2  X  X  X  0  X  X  2  1  1  0  1  1  1  1  1  1  2 X+2  X  X  X  X  X  0  2  1  1  1  1  1  1  1  1  2  2  0  0  X  2  X  X  X
 0  1 X+1 X+2  3  1  2 X+3  1  X  1  1  0 X+1  1 X+2  3  1  2 X+3  1  X  1  1  0 X+1  1 X+2  3  1  2 X+3  1  X  1  1  0 X+1  1 X+2  3  1  2  X X+3  1  1  1  0 X+2  X  2  X  X  0 X+1  1 X+2 X+3  2  X  3  1  1  1  1  0  2 X+2  X  X  X  0  2 X+1 X+3 X+2  X  3  1  0  2  2  1  0  1  2 X+2  X

generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+56x^90+4x^92+3x^96

The gray image is a code over GF(2) with n=356, k=6 and d=180.
This code was found by Heurico 1.16 in 0.254 seconds.