The generator matrix

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

generates a code of length 16 over Z2[X]/(X^4) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+140x^13+484x^14+770x^15+1347x^16+752x^17+456x^18+108x^19+12x^20+20x^21+4x^22+2x^23

The gray image is a linear code over GF(2) with n=128, k=12 and d=52.
This code was found by Heurico 1.16 in 0.046 seconds.