The generator matrix

 1  1  1  1  1  X  1  1  X  X  X  1
 0  X  0  X  0  0  X  2  2  2  2 X+2
 0  0  X  X  0  X  X  X  X  X  X  0
 0  0  0  2  0  0  0  0  0  2  2  2
 0  0  0  0  2  0  0  2  0  2  2  0
 0  0  0  0  0  2  0  0  2  2  2  0
 0  0  0  0  0  0  2  0  2  2  0  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+183x^8+256x^10+1168x^12+256x^14+183x^16+1x^24

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 4.38 seconds.