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 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 X 1 1 1 1
0 2X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2X 0 2X 2X 0 2X 2X 0 2X 2X 2X 0 2X 0 2X 2X 0 2X 2X 2X 2X 0 2X 2X 0 0 2X 2X 0 0 2X 2X 2X 0 0 2X 0 0 2X 0 0 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 2X 2X 0
0 0 2X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2X 2X 2X 0 2X 2X 0 2X 2X 0 2X 2X 0 2X 0 2X 2X 0 2X 2X 0 2X 2X 0 2X 2X 2X 0 2X 2X 2X 2X 0 0 2X 0 2X 2X 2X 2X 2X 2X 2X 0 2X 0 0 0 0 0 0 0 2X 0 2X 2X 0
0 0 0 2X 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 0 2X 2X 2X 2X 0 2X 2X 0 2X 2X 0 0 2X 2X 0 2X 0 2X 0 0 0 2X 2X 0 2X 2X 0 2X 0 0 2X 2X 2X 0 2X 2X 0 0 0 0 0 2X 0 2X 2X 0 0 0 0 0 0 0 2X 0 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 2X 2X 2X 2X 0 0 2X 0 2X 2X 2X 2X 2X 0 0 0 0 2X 0 0 2X 0 2X 0 2X 0 2X 2X 2X 2X 0 2X 0 2X 2X 2X 2X 0 2X 0 0 0 0 2X 2X 2X 0 2X 0
0 0 0 0 0 2X 0 2X 2X 2X 0 0 0 0 2X 2X 2X 0 0 0 0 0 0 2X 2X 2X 0 0 2X 2X 2X 0 2X 2X 2X 0 0 0 2X 2X 0 2X 0 2X 0 2X 0 2X 0 2X 2X 0 2X 0 0 2X 2X 2X 0 2X 2X 2X 2X 0 2X 0 0 2X 2X 2X 0 0 0 0
0 0 0 0 0 0 2X 2X 0 2X 2X 0 2X 2X 2X 0 0 0 0 0 0 2X 2X 2X 2X 0 0 0 0 2X 0 2X 2X 2X 2X 2X 0 2X 0 2X 2X 2X 0 0 2X 0 2X 2X 2X 0 2X 2X 2X 2X 0 0 2X 0 2X 2X 0 0 0 0 0 0 2X 2X 0 0 0 0 0 0
generates a code of length 74 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 68.
Homogenous weight enumerator: w(x)=1x^0+13x^68+82x^72+832x^74+82x^76+12x^80+1x^84+1x^144
The gray image is a code over GF(2) with n=592, k=10 and d=272.
This code was found by Heurico 1.16 in 0.281 seconds.