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

generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 91.

Homogenous weight enumerator: w(x)=1x^0+22x^91+2x^92+4x^94+2x^95+1x^96

The gray image is a code over GF(2) with n=356, k=5 and d=182.
This code was found by Heurico 1.16 in 0.381 seconds.