The generator matrix

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

generates a code of length 12 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+181x^8+64x^9+778x^10+448x^11+1141x^12+448x^13+812x^14+64x^15+146x^16+10x^18+3x^20

The gray image is a code over GF(2) with n=48, k=12 and d=16.
This code was found by Heurico 1.11 in 0.0232 seconds.