The generator matrix

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

generates a code of length 16 over Z2[X]/(X^4) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+17x^12+32x^13+69x^14+32x^15+729x^16+32x^17+62x^18+32x^19+10x^20+5x^22+2x^24+1x^28

The gray image is a linear code over GF(2) with n=128, k=10 and d=48.
This code was found by Heurico 1.16 in 1.05e-007 seconds.