The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1
 0  X  0 X^3+X^2+X X^3 X^2+X  0  X X^2 X^3+X^2+X X^2+X X^3+X^2 X^3+X  X  0  0
 0  0 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2 X^2 X^2 X^2  0 X^3  0 X^3 X^3  0
 0  0  0 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3  0  0 X^3 X^3 X^3+X^2 X^2  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+30x^12+82x^13+101x^14+300x^15+1015x^16+312x^17+104x^18+68x^19+26x^20+6x^21+2x^22+1x^30

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 0.031 seconds.