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  X  1  X  X  X  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  X  X  X  X  X  X  X  X  X  X  X  X 2X  0  X  0 2X 2X+2  X  0 2X+2
 0  2  0 2X+2  0  0 2X+2  2  0  0 2X+2  2  0  0 2X+2  2  0  0 2X+2  2  0  0 2X+2  2  0  0 2X+2  2  0  0 2X+2 2X  2 2X 2X 2X 2X  2 2X 2X+2 2X  2 2X 2X+2 2X  2 2X 2X+2 2X  2 2X 2X+2 2X 2X  2 2X+2 2X 2X  2 2X+2 2X 2X  2 2X+2 2X 2X  2 2X+2 2X+2 2X+2  2  2  2 2X+2  2  0  2 2X+2  2  2  0  0 2X+2 2X+2 2X+2  0 2X+2  2  0  0  0
 0  0  2 2X+2  0  2 2X+2  0  0  2 2X+2  0  0  2 2X+2  0 2X 2X+2  2 2X 2X 2X+2  2 2X 2X 2X+2  2 2X 2X 2X+2  2 2X+2 2X 2X+2 2X+2 2X+2 2X  2 2X+2 2X 2X  2 2X+2 2X 2X  2 2X+2 2X 2X  2 2X+2 2X  0  2 2X+2  0  0  2 2X+2  0  0  2 2X+2  0  0  2 2X+2  0 2X+2  2  0 2X  2 2X+2 2X+2  2  0  0  0  2 2X+2  0  2 2X 2X 2X+2  2 2X  0 2X+2  0
 0  0  0 2X  0  0 2X  0 2X 2X  0 2X 2X 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0  0  0  0 2X 2X  0  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0  0  0  0  0 2X 2X  0  0  0 2X 2X  0 2X 2X 2X  0 2X  0  0  0  0 2X 2X  0
 0  0  0  0 2X 2X 2X 2X 2X 2X  0 2X  0  0 2X  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0 2X 2X  0  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  0  0  0 2X 2X 2X 2X  0 2X 2X  0  0  0 2X  0 2X 2X 2X  0  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+302x^88+208x^90+340x^92+48x^94+110x^96+12x^100+2x^104+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 2.34 seconds.