The generator matrix
1 0 0 1 1
0 1 0 1 0
0 0 1 1 0
0 0 0 2 0
generates a code of length 5 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+87x^2+420x^3+1096x^4+4984x^5+1096x^6+420x^7+87x^8+1x^10
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 -3.24e-008 seconds.