The generator matrix
1 1 1 1 1 1 X 1
0 X 0 0 0 0 X 0
0 0 X 0 0 0 X 0
0 0 0 X 0 0 X 0
0 0 0 0 X 0 X 0
0 0 0 0 0 X X 0
0 0 0 0 0 0 2 0
generates a code of length 8 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+66x^2+24x^3+496x^4+440x^5+990x^6+3632x^7+5086x^8+3632x^9+990x^10+440x^11+496x^12+24x^13+66x^14+1x^16
The gray image is a code over GF(2) with n=32, k=14 and d=4.
This code was found by Heurico 1.16 in 0.105 seconds.