The generator matrix

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

generates a code of length 18 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+164x^14+372x^15+550x^16+576x^17+768x^18+632x^19+526x^20+320x^21+144x^22+20x^23+19x^24+4x^26

The gray image is a code over GF(2) with n=72, k=12 and d=28.
This code was found by Heurico 1.11 in 0.0553 seconds.