The generator matrix

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

generates a code of length 11 over Z2[X]/(X^4) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+3x^10+54x^11+3x^12+1x^14+2x^15

The gray image is a linear code over GF(2) with n=88, k=6 and d=40.
This code was found by Heurico 1.16 in -6.48e-008 seconds.