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.