The generator matrix
1 0 0 1 1 1
0 1 0 X 2X+3 0
0 0 1 1 X+1 0
0 0 0 2X 0 2X
generates a code of length 6 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 3.
Homogenous weight enumerator: w(x)=1x^0+54x^3+306x^4+1322x^5+4828x^6+1322x^7+301x^8+54x^9+4x^10
The gray image is a code over GF(2) with n=48, k=13 and d=12.
This code was found by Heurico 1.16 in 0.016 seconds.