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 1 1 1 1 1 1 1 1 1 X X 1 1 1
0 2X 0 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 0 2X 2X 0 2X 2X 0 2X 2X 0 2X 2X 0 2X 2X 0 2X 2X 0 2X 2X 0 2X 0 2X 0 2X 0 0 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 0 2X 2X 0 2X 2X 0 0
0 0 2X 0 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 2X 0 2X 0 2X 2X 2X 0 2X 0 2X 2X 2X 0 2X 2X 2X 2X 0 2X 2X 2X 2X 2X 2X 0 2X 2X 0 0 0 0 0 0 0 0 0 0 2X 2X 0 2X 2X 0 0 0
0 0 0 2X 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 0 2X 2X 2X 2X 0 2X 0 2X 2X 2X 0 2X 2X 2X 2X 0 2X 0 0 2X 0 2X 0 0 0 2X 2X 2X 0 2X 2X 0 0 0 0 0 2X 0 2X 2X 2X 0 0 0 0 0 0 0 0 2X 2X 2X 0 2X 2X 2X 0 0 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 0 2X 2X 2X 0 2X 0 2X 2X 2X 0 2X 2X 2X 0 2X 2X 0 0 2X 0 2X 2X 2X 2X 0 0 2X 2X 2X 2X 2X 0 0 0 0 0 2X 2X 0 0 0 0 2X 2X 0 0 0
0 0 0 0 0 2X 0 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 0 0 0 0 0 0 0 2X 2X 0 2X 2X 0 2X 2X 0 2X 0 2X 0 2X 2X 2X 0 2X 2X 0 2X 2X 0 0 2X 2X 2X 0 2X 2X 0 0 2X 0 2X 2X 2X 0 0 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0
0 0 0 0 0 0 2X 2X 0 2X 2X 0 2X 2X 2X 0 0 2X 0 0 0 0 2X 2X 2X 2X 2X 2X 0 2X 0 2X 0 0 0 2X 2X 2X 0 0 0 2X 2X 0 2X 2X 0 0 0 2X 2X 2X 0 0 0 2X 2X 0 2X 2X 2X 0 0 2X 0 2X 2X 0 0 0 0 0 0 2X 2X 0 0 0
generates a code of length 78 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 72.
Homogenous weight enumerator: w(x)=1x^0+26x^72+68x^76+832x^78+73x^80+20x^84+3x^88+1x^152
The gray image is a code over GF(2) with n=624, k=10 and d=288.
This code was found by Heurico 1.16 in 0.343 seconds.