The generator matrix

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

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+36x^4+32x^5+160x^6+480x^7+630x^8+480x^9+160x^10+32x^11+36x^12+1x^16

The gray image is a code over GF(2) with n=32, k=11 and d=8.
This code was found by Heurico 1.16 in 0.00259 seconds.