The generator matrix

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

generates a code of length 18 over Z4[X]/(X^3+2,2X) 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 code over GF(2) with n=144, k=12 and d=56.
This code was found by Heurico 1.16 in 0.062 seconds.