The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1
 0 X^3+X^2  0 X^3+X^2  0 X^3 X^3+X^2 X^2  0 X^3+X^2  0 X^3 X^3+X^2 X^3  0  0
 0  0 X^3  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0
 0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0
 0  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3  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+11x^12+8x^13+12x^14+28x^15+401x^16+20x^17+14x^18+4x^19+3x^20+4x^21+5x^22+1x^30

The gray image is a linear code over GF(2) with n=128, k=9 and d=48.
This code was found by Heurico 1.16 in -3.24e-008 seconds.