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 2X  X 2X+2  X 2X  X 2X+2  X  0  X 2X  X  2  X  0  X 2X 2X+2  X  0 2X+2  X 2X+2  X  X  X
 0  X  0 3X+2 2X+2 X+2  2  X  0 3X+2  0 X+2 2X+2  X  2  X  0 3X+2  0 X+2 2X+2  X  2  X  0 3X+2  0 X+2 2X+2  X  2  X 2X X+2 2X 3X+2  2 3X 2X+2 3X 2X X+2 2X+2 3X 2X 3X+2  2 3X 2X X+2 2X+2 3X 2X 3X+2  2 3X 2X X+2 2X+2 3X 2X 3X+2  2 3X 3X+2  X 3X  X 3X+2  X 3X  X X+2  X 3X+2  X  X  X 3X  X 3X+2  X 2X 3X  X  X  X  X  0  X 2X
 0  0  2  0  2 2X+2  0 2X+2 2X 2X 2X+2  2 2X+2  2 2X 2X  0  0  2 2X+2 2X+2  2 2X 2X 2X 2X 2X+2  2  2 2X+2  0  0 2X 2X 2X+2  2  2 2X+2  0  0  0  0 2X 2X  2 2X+2 2X+2  2 2X 2X 2X 2X 2X+2  2 2X+2  2  0  0  0  0  2 2X+2  2 2X+2  0 2X+2  0  2 2X  2 2X 2X+2 2X+2  0  2 2X 2X+2  0  2 2X  0 2X+2  2 2X  2 2X+2  0 2X  0 2X+2  2
 0  0  0 2X 2X  0 2X 2X  0 2X  0  0 2X 2X 2X  0 2X  0 2X 2X  0  0  0 2X 2X  0 2X 2X  0  0  0 2X  0  0  0  0 2X 2X 2X 2X  0  0 2X 2X  0  0 2X 2X 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0  0  0 2X 2X  0  0 2X 2X  0  0  0  0 2X 2X 2X 2X 2X 2X  0  0 2X  0  0  0 2X  0  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+184x^88+376x^90+272x^92+136x^94+52x^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 1.22 seconds.