The generator matrix

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

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+86x^14+16x^15+186x^16+112x^17+244x^18+112x^19+167x^20+16x^21+54x^22+29x^24+1x^28

The gray image is a code over GF(2) with n=72, k=10 and d=28.
This code was found by Heurico 1.16 in 0.0152 seconds.