The generator matrix

 1  1  1  1  1  1  1  1  1  1  X X^3  1  X  1  1
 0  X  0 X^2+X X^2 X^3+X^2+X X^3+X^2  X  0 X^2+X X^3+X^2+X  X X^3+X^2 X^3 X^3+X^2+X  0
 0  0 X^3+X^2  0 X^2 X^2 X^3 X^2  0 X^3 X^2 X^2  0 X^2 X^3 X^3
 0  0  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3  0 X^3 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+42x^13+80x^14+210x^15+360x^16+236x^17+61x^18+12x^19+6x^20+10x^21+2x^22+2x^23+1x^24+1x^26

The gray image is a linear code over GF(2) with n=128, k=10 and d=52.
This code was found by Heurico 1.16 in -6.48e-008 seconds.