The generator matrix

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

generates a code of length 16 over Z2[X]/(X^4) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+304x^11+1751x^12+7518x^13+25434x^14+57222x^15+77246x^16+57932x^17+25420x^18+7292x^19+1673x^20+278x^21+58x^22+14x^23+1x^24

The gray image is a linear code over GF(2) with n=128, k=18 and d=44.
This code was found by Heurico 1.16 in 82.5 seconds.