The generator matrix

 1  0  0  0  1  1
 0  1  0  0 X+1  0
 0  0  1  0  1  0
 0  0  0  1  1  0
 0  0  0  0 X^3  0

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+172x^2+1456x^3+7175x^4+20944x^5+71576x^6+20944x^7+7175x^8+1456x^9+172x^10+1x^12

The gray image is a linear code over GF(2) with n=48, k=17 and d=8.
This code was found by Heurico 1.16 in 2.48 seconds.