The generator matrix

 1  0  0  0  1  1  1 X^3+X X^2+X  1  1 X^3 X^2  1  1  1
 0  1  0  0 X^2 X^3+1 X^2+1  1  1 X^2+X X^3+X  1 X^3+X X^2+1 X^3  X
 0  0  1  0 X^2+1  1 X^2 X^2+X+1  1 X+1  0 X^3+X  1 X^2+X X^2+1 X^3
 0  0  0  1  1 X^2 X^2+X+1 X^2+X+1 X^3+X^2+X X^3 X^3+X^2+1 X^3+X+1 X+1 X^2+X X+1  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+452x^12+1998x^13+6316x^14+14820x^15+18219x^16+15100x^17+6296x^18+1832x^19+448x^20+38x^21+12x^22+4x^23

The gray image is a linear code over GF(2) with n=128, k=16 and d=48.
This code was found by Heurico 1.16 in 7.34 seconds.