The generator matrix

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

generates a code of length 8 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+31x^4+120x^5+432x^6+872x^7+1111x^8+968x^9+448x^10+88x^11+25x^12

The gray image is a code over GF(2) with n=32, k=12 and d=8.
This code was found by Heurico 1.11 in 0.00264 seconds.