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

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+232x^88+256x^90+344x^92+160x^94+28x^96+2x^112+1x^128

The gray image is a code over GF(2) with n=728, k=10 and d=352.
This code was found by Heurico 1.16 in 0.907 seconds.