The generator matrix

 1  0  0  1  1
 0  1  0  X 2X+3
 0  0  1  1 X+1

generates a code of length 5 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+128x^3+738x^4+2368x^5+728x^6+128x^7+5x^8

The gray image is a code over GF(2) with n=40, k=12 and d=12.
This code was found by Heurico 1.16 in 5.34e-008 seconds.