The generator matrix

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

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+92x^12+64x^13+504x^14+704x^15+1385x^16+704x^17+480x^18+64x^19+84x^20+8x^22+6x^24

The gray image is a linear code over GF(2) with n=128, k=12 and d=48.
This code was found by Heurico 1.16 in 0.062 seconds.