The generator matrix

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

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+1x^10+24x^11+1x^12+4x^13+1x^14

The gray image is a code over GF(2) with n=88, k=5 and d=40.
This code was found by Heurico 1.16 in 0 seconds.