The generator matrix

 1  1  1  1  1  1  1  1  X  X  2  1
 0  X  0  0  0  0  0  2 X+2 X+2  2 X+2
 0  0  X  0  0  2 X+2  X X+2  0  X X+2
 0  0  0  X  0 X+2 X+2  X  0  2  2  0
 0  0  0  0  X  X  2 X+2 X+2  0 X+2 X+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+86x^8+200x^9+76x^10+480x^11+144x^12+784x^13+168x^14+32x^15+25x^16+40x^17+12x^18

The gray image is a code over GF(2) with n=48, k=11 and d=16.
This code was found by Heurico 1.16 in 0.0202 seconds.