The generator matrix

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

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+54x^8+160x^10+128x^11+340x^12+128x^13+160x^14+49x^16+4x^20

The gray image is a code over GF(2) with n=48, k=10 and d=16.
This code was found by Heurico 1.16 in 0.005 seconds.