The generator matrix

 1  0  1  1  1 X+2  1  1  X  1  1
 0  1 X+1 X+2  3  1  2 X+2  0 X+3 X+1
 0  0  2  0  2  0  0  2  2  2  0

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

Homogenous weight enumerator: w(x)=1x^0+71x^10+46x^12+8x^14+1x^16+1x^18

The gray image is a code over GF(2) with n=44, k=7 and d=20.
This code was found by Heurico 1.16 in 0.00056 seconds.