The generator matrix
1 1 1 1 X 1 1 1
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 0 0
0 0 0 0 0 2 0 0
0 0 0 0 0 0 2 0
0 0 0 0 0 0 0 2
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+32x^2+188x^4+128x^5+480x^6+1920x^7+2694x^8+1920x^9+480x^10+128x^11+188x^12+32x^14+1x^16
The gray image is a code over GF(2) with n=32, k=13 and d=4.
This code was found by Heurico 1.16 in 0.0281 seconds.