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 X X X X X X X X X X X X 1 X X X X 1 1 1 X X X X X X X X X X X 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
0 2X+2 0 2X+2 0 2X+2 0 2X+2 0 2X+2 0 2X+2 0 2X+2 0 2X+2 2X 2 2X 2 2X 2 2X 2 2X 2 2X 2 2X 2 2X 2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 0 2X 0 2X 0 0 2X 0 2X 0 0 0 2X 2X 2 2X 2 2 2 2 2 2 2 0 0 0 2X+2 2X+2 2X+2 2X+2 0 2X+2 0 2X+2 2X 2 2X 2 2X 2 0 2X 2 2 2 2X+2 2X+2 2X 2X 2 0
0 0 2X 0 0 0 2X 0 0 2X 0 2X 2X 2X 2X 2X 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 0 0 0 0 2X 2X 2X 2X 0 2X 2X 2X 2X 2X 0 2X 0 0 2X 2X 0 0 0 2X 2X 0 0 2X 2X 0 0 0 0 2X 0 0 2X 2X 0 2X 0 2X 0 0 2X 2X 2X 0 2X 0
0 0 0 2X 0 0 0 2X 2X 2X 2X 2X 2X 0 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 0 2X 2X 0 0 2X 2X 0 0 2X 0 2X 2X 2X 0 0 2X 2X 0 2X 2X 0 0 2X 2X 0 0 0 2X 2X 0 2X 2X 0 2X 2X 2X 2X 2X 0 0 2X 0 2X 0 0 0
0 0 0 0 2X 2X 2X 2X 2X 0 0 2X 0 2X 2X 0 0 0 2X 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 0 0 2X 2X 0 2X 2X 2X 2X 0 0 0 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 0 0 2X 2X 2X 2X 2X 2X 2X 0 2X 2X 0 2X 0 0 2X 2X 0 0 0 2X 2X 0 0
generates a code of length 91 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 89.
Homogenous weight enumerator: w(x)=1x^0+46x^89+23x^90+384x^91+24x^92+16x^93+8x^94+7x^96+2x^121+1x^122
The gray image is a code over GF(2) with n=728, k=9 and d=356.
This code was found by Heurico 1.16 in 0.875 seconds.