The generator matrix

 1  0  0  1  1  1  X  1  1  1
 0  1  0  1 X+2 X+3  1  0  0  0
 0  0  1  1 X+3 X+2  1  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+68x^4+128x^5+232x^6+512x^7+2270x^8+1408x^9+7160x^10+1408x^11+2228x^12+512x^13+280x^14+128x^15+41x^16+8x^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 0.13 seconds.