The generator matrix

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

generates a code of length 16 over Z2[X]/(X^4) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+108x^11+888x^12+4138x^13+11837x^14+29610x^15+37499x^16+30276x^17+11895x^18+3776x^19+844x^20+178x^21+11x^22+10x^23+1x^26

The gray image is a linear code over GF(2) with n=128, k=17 and d=44.
This code was found by Heurico 1.16 in 19.3 seconds.