The generator matrix

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

generates a code of length 18 over Z2[X]/(X^4) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+87x^16+136x^17+150x^18+16x^19+72x^20+40x^21+8x^22+2x^26

The gray image is a linear code over GF(2) with n=144, k=9 and d=64.
This code was found by Heurico 1.16 in -1.01e-007 seconds.