The generator matrix

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

generates a code of length 12 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+12x^10+32x^11+38x^12+32x^13+11x^14+1x^16+1x^22

The gray image is a code over GF(2) with n=48, k=7 and d=20.
This code was found by Heurico 1.16 in 0.000684 seconds.