The generator matrix

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

generates a code of length 16 over Z2[X]/(X^4) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+24x^10+60x^12+104x^14+1677x^16+104x^18+44x^20+24x^22+10x^24

The gray image is a linear code over GF(2) with n=128, k=11 and d=40.
This code was found by Heurico 1.16 in 0.25 seconds.