The generator matrix

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

generates a code of length 10 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+20x^7+98x^8+32x^9+192x^10+72x^11+88x^12+4x^15+5x^16

The gray image is a code over GF(2) with n=40, k=9 and d=14.
This code was found by Heurico 1.16 in 0.0186 seconds.