The generator matrix

 1  1  X  1  1  1
 0 X^3+X^2 X^3+X^2  0  0 X^3
 0  0 X^3  0 X^3 X^3
 0  0  0 X^3 X^3  0

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+12x^4+32x^5+166x^6+32x^7+11x^8+2x^10

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 -1.01e-007 seconds.