The generator matrix

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

generates a code of length 18 over Z4[X]/(X^2+2X+2) 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 code over GF(2) with n=144, k=12 and d=56.
This code was found by Heurico 1.16 in 0.047 seconds.