The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+80x^14+142x^16+512x^17+608x^18+512x^19+96x^20+80x^22+16x^24+1x^32

The gray image is a code over GF(2) with n=144, k=11 and d=56.
This code was found by Heurico 1.16 in 0.046 seconds.