The generator matrix

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

generates a code of length 9 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+76x^4+128x^5+392x^6+2304x^7+1614x^8+7424x^9+1488x^10+2304x^11+476x^12+128x^13+40x^14+9x^16

The gray image is a code over GF(2) with n=36, k=14 and d=8.
This code was found by Heurico 1.16 in 0.129 seconds.