The generator matrix
1 1 1 1 1 1
0 X^3 0 0 0 X^3
0 0 X^3 0 0 X^3
0 0 0 X^3 0 X^3
0 0 0 0 X^3 X^3
generates a code of length 6 over Z2[X]/(X^4) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+15x^4+224x^6+15x^8+1x^12
The gray image is a linear code over GF(2) with n=48, k=8 and d=16.
This code was found by Heurico 1.16 in 6.87e-008 seconds.