The generator matrix

 1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1
 0 X^3  0  0  0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0
 0  0 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0  0
 0  0  0 X^3  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0
 0  0  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0
 0  0  0  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0  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+16x^12+11x^14+32x^15+395x^16+32x^17+12x^18+4x^20+8x^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 -1.01e-007 seconds.