The generator matrix

 1  1  1  1  1  1  1  X X^3  1  X  X X^2  X  X  X
 0  X  0 X^2+X X^2 X^3+X^2+X X^3+X^2 X^3+X^2+X  X X^3+X^2+X X^2+X X^3+X X^2 X^2 X^2 X^3+X^2
 0  0 X^3+X^2  0 X^2 X^2 X^3 X^3+X^2 X^2 X^2  0 X^3 X^2 X^2 X^3  0
 0  0  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0
 0  0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0  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+74x^12+16x^13+360x^14+240x^15+683x^16+240x^17+336x^18+16x^19+70x^20+8x^22+4x^24

The gray image is a linear code over GF(2) with n=128, k=11 and d=48.
This code was found by Heurico 1.16 in 0.032 seconds.