The generator matrix

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

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+22x^12+52x^13+129x^14+176x^15+217x^16+264x^17+119x^18+16x^19+14x^20+4x^21+7x^22+2x^24+1x^26

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 3.62e-008 seconds.