The generator matrix

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

generates a code of length 18 over Z2[X]/(X^4) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+16x^14+140x^15+393x^16+1088x^17+850x^18+1072x^19+384x^20+120x^21+12x^22+4x^23+6x^24+8x^25+2x^26

The gray image is a linear code over GF(2) with n=144, k=12 and d=56.
This code was found by Heurico 1.16 in 0.031 seconds.