The generator matrix

 1  0  1  1  1  0  1  1  X  1
 0  1 X+1 X+2  1  1  0  0  0  0
 0  0  2  0  0  0  0  0  2  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+36x^4+32x^5+40x^6+160x^7+382x^8+832x^9+1144x^10+832x^11+340x^12+160x^13+88x^14+32x^15+9x^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 0.00972 seconds.