The generator matrix

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

generates a code of length 16 over Z2[X]/(X^4) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+118x^14+288x^15+283x^16+192x^17+100x^18+32x^19+4x^20+6x^22

The gray image is a linear code over GF(2) with n=128, k=10 and d=56.
This code was found by Heurico 1.16 in 0.078 seconds.