The generator matrix

 1  1  1  1  1  1  1  1  X  1
 0  X  0  0  0  0  0 X+2  2  0
 0  0  X  0  0  0  0  X  X  2
 0  0  0  X  0  0  0  X X+2  2
 0  0  0  0  X  0  X  0  2  0
 0  0  0  0  0  X  X  0  X  2
 0  0  0  0  0  0  2  2  0  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+55x^4+146x^5+261x^6+580x^7+993x^8+3390x^9+5581x^10+3320x^11+965x^12+622x^13+295x^14+132x^15+34x^16+2x^17+7x^18

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 0.244 seconds.