The generator matrix

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

generates a code of length 11 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+3x^10+54x^11+3x^12+1x^14+2x^15

The gray image is a code over GF(2) with n=88, k=6 and d=40.
This code was found by Heurico 1.16 in -3.24e-008 seconds.