The generator matrix

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

generates a code of length 10 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+85x^4+432x^6+128x^7+2858x^8+1920x^9+5536x^10+1920x^11+2858x^12+128x^13+432x^14+85x^16+1x^20

The gray image is a code over GF(2) with n=40, k=14 and d=8.
This code was found by Heurico 1.16 in 0.175 seconds.