The generator matrix

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

generates a code of length 10 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+62x^6+48x^7+332x^8+208x^9+748x^10+208x^11+332x^12+48x^13+54x^14+7x^16

The gray image is a code over GF(2) with n=40, k=11 and d=12.
This code was found by Heurico 1.16 in 0.00653 seconds.