The generator matrix

 1  0  0  1  1  1  2  1  1 X+2  1  1  0  2  0  X  1  1  X X+2  1  1  1  1  1  X  1  0  1  1 X+2  1  1 X+2  1  1  X  1  1  2  1  2  2  1  X  2  2  1  X  1 X+2 X+2  1  0  1  0 X+2  1  1  X X+2  2  1  2  1  1 X+2  X  1  2  0  1  X  1  1  1  0  1  X  1  1  2  1  1 X+2  0  1  1  X  1 X+2
 0  1  0  2  3  1  1  0  2  0  3  1  1  1 X+2  X  X X+1  1  1 X+2 X+3 X+2  0 X+3  1  3  1  X X+1  1  X X+3  1 X+2 X+1  1  2  1  1  2  1  2  2  2  1  X X+2  1  X X+2  1  0  1  3  2  X  2  2  1  1 X+2  X  1 X+3  1  2  0  3  0  X  3 X+2 X+3 X+1 X+2  1  X  1  X  2  1  0 X+2  1  1  0 X+1 X+2 X+2  1
 0  0  1 X+3 X+1  2 X+1 X+2  1  1  3  X X+2  3  1  1  X X+1  3  X X+3  0  0 X+3  1  0  2  3 X+1  2  1  1 X+2 X+3  3  X X+1  3 X+2 X+3  2  2  1  X  1  X  1 X+2 X+2  2  1  2  1 X+1  0  1  1  0 X+2  X  0  1 X+2  0  2  0  1  1  X  1  1 X+2  1  X  0  2  X  3  2 X+3 X+1 X+2  3  1 X+1  2 X+1 X+2  0 X+1 X+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+88x^89+156x^90+104x^91+58x^92+48x^93+36x^94+8x^95+2x^96+8x^97+2x^108+1x^128

The gray image is a code over GF(2) with n=364, k=9 and d=178.
This code was found by Heurico 1.16 in 20.3 seconds.