The generator matrix
1 1 1 1 1 1 1 X 1 X X 1 2 0 X 1 2 1
0 2 0 2 0 2 0 2 2 0 2 0 2 2 0 2 0 0
generates a code of length 18 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 18.
Homogenous weight enumerator: w(x)=1x^0+1x^18+12x^19+1x^20+1x^22
The gray image is a code over GF(2) with n=72, k=4 and d=36.
This code was found by Heurico 1.16 in 0.00105 seconds.