The generator matrix

 1  1  1  1  X  X  X  1  1  1
 0  X  0  X  0  X  X  0  0  0
 0  0  X  X  X  X  0  0  0  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  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+52x^4+104x^6+128x^7+622x^8+384x^9+1528x^10+384x^11+580x^12+128x^13+152x^14+25x^16+8x^18

The gray image is a code over GF(2) with n=40, k=12 and d=8.
This code was found by Heurico 1.16 in 0.0132 seconds.