The generator matrix

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

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+65x^4+42x^5+242x^6+260x^7+469x^8+1742x^9+2544x^10+1752x^11+463x^12+262x^13+250x^14+36x^15+58x^16+2x^17+4x^18

The gray image is a code over GF(2) with n=40, k=13 and d=8.
This code was found by Heurico 1.16 in 0.0681 seconds.