The generator matrix

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

generates a code of length 91 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+388x^88+272x^89+296x^90+280x^91+328x^92+104x^93+208x^94+104x^95+24x^96+8x^97+24x^98+4x^100+5x^104+1x^128+1x^136

The gray image is a code over GF(2) with n=728, k=11 and d=352.
This code was found by Heurico 1.16 in 3.73 seconds.