The generator matrix
1 1 X 1 1 1
0 2 0 0 2 0
0 0 2 0 2 0
0 0 0 2 2 0
generates a code of length 6 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+6x^4+8x^5+100x^6+8x^7+1x^8+4x^10
The gray image is a code over GF(2) with n=48, k=7 and d=16.
This code was found by Heurico 1.16 in -6.48e-008 seconds.