The generator matrix

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

generates a code of length 10 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+10x^8+34x^9+44x^10+28x^11+5x^12+2x^13+3x^14+1x^18

The gray image is a code over GF(2) with n=40, k=7 and d=16.
This code was found by Heurico 1.16 in 0.000381 seconds.