The generator matrix

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

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+76x^14+174x^15+453x^16+780x^17+1150x^18+828x^19+388x^20+112x^21+100x^22+22x^23+6x^24+4x^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 0.063 seconds.