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

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

Homogenous weight enumerator: w(x)=1x^0+106x^89+23x^90+16x^91+24x^92+56x^93+8x^94+6x^96+12x^97+2x^105+1x^106+1x^112

The gray image is a code over GF(2) with n=364, k=8 and d=178.
This code was found by Heurico 1.16 in 65.9 seconds.