The generator matrix

 1  1  1  1  X  X
 0  X X^3+X^2 X^2+X X^2+X X^2+X
 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+87x^4+128x^5+592x^6+128x^7+87x^8+1x^12

The gray image is a linear code over GF(2) with n=48, k=10 and d=16.
This code was found by Heurico 1.16 in 0 seconds.