The generator matrix
1 0 1 1 1 1
0 1 X+1 0 0 0
0 0 X^3 0 0 0
0 0 0 X^3 0 0
0 0 0 0 X^3 0
0 0 0 0 0 X^3
generates a code of length 6 over Z2[X]/(X^4) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+34x^2+127x^4+448x^5+2876x^6+448x^7+127x^8+34x^10+1x^12
The gray image is a linear code over GF(2) with n=48, k=12 and d=8.
This code was found by Heurico 1.16 in -3.24e-008 seconds.