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 X X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 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
0 2X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2X 0 2X 0 2X 0 2X 0 2X 2X 2X 0 2X 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 2X 2X 0 0 2X 0 2X 2X 2X 2X 0 0 2X 0 2X 2X 2X 2X 2X 2X 0 0 0 0 0
0 0 2X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2X 0 2X 0 2X 0 2X 0 2X 0 2X 2X 2X 0 2X 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 2X 2X 0 0 2X 2X 0 2X 2X 2X 0 0 2X 2X 2X 2X 0 2X 0 0 2X 2X 0 0 0 2X 2X
0 0 0 2X 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 0 2X 2X 2X 2X 0 0 0 0 0 0 0 0 0 0 0 0 2X 2X 2X 2X 0 2X 2X 0 0 2X 0 2X 0 2X 2X 2X 0 2X 0 0 0 2X 0 2X 0 2X 2X 0 0 2X 2X 0
0 0 0 0 2X 0 0 0 2X 2X 2X 2X 2X 0 2X 2X 0 0 0 0 0 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 0 2X 0 2X 0 2X 2X 0 2X 0 2X 2X 2X 2X 0 2X 2X 2X 0 2X 0 2X 2X 2X 0 0 2X 2X 2X 2X 0 2X 0 0 2X 2X 0 2X
0 0 0 0 0 2X 0 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 0 0 0 0 0 2X 0 2X 2X 0 0 2X 2X 0 2X 2X 0 2X 2X 2X 2X 0 2X 2X 0 2X 2X 0 2X 2X 2X 2X 0 0 2X 0 2X 2X 0 0 0 0
0 0 0 0 0 0 2X 2X 0 2X 2X 0 2X 2X 2X 0 0 2X 0 0 2X 2X 2X 2X 2X 2X 0 0 0 2X 0 0 2X 2X 0 0 2X 2X 2X 2X 0 0 2X 2X 2X 0 0 2X 2X 2X 2X 2X 0 0 0 2X 0 2X 2X 0 0 0 0 0 0 2X 2X 2X 2X 0 0 0
generates a code of length 72 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 68.
Homogenous weight enumerator: w(x)=1x^0+56x^68+908x^72+56x^76+2x^80+1x^128
The gray image is a code over GF(2) with n=576, k=10 and d=272.
This code was found by Heurico 1.16 in 80.2 seconds.