The generator matrix

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

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+103x^12+492x^13+1610x^14+3518x^15+4923x^16+3596x^17+1556x^18+448x^19+115x^20+8x^21+10x^22+2x^23+2x^24

The gray image is a linear code over GF(2) with n=128, k=14 and d=48.
This code was found by Heurico 1.16 in 0.516 seconds.