The generator matrix

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

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+268x^13+958x^14+1520x^15+2739x^16+1544x^17+860x^18+240x^19+44x^20+12x^21+6x^22

The gray image is a linear code over GF(2) with n=128, k=13 and d=52.
This code was found by Heurico 1.16 in 1.33 seconds.