The generator matrix

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

generates a code of length 13 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+36x^8+108x^9+188x^10+468x^11+800x^12+888x^13+802x^14+488x^15+183x^16+92x^17+32x^18+4x^19+4x^20+2x^22

The gray image is a code over GF(2) with n=52, k=12 and d=16.
This code was found by Heurico 1.16 in 0.048 seconds.