The generator matrix

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

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+161x^8+176x^9+1096x^10+1600x^11+3354x^12+3616x^13+3328x^14+1600x^15+1141x^16+176x^17+120x^18+14x^20+1x^24

The gray image is a code over GF(2) with n=52, k=14 and d=16.
This code was found by Heurico 1.16 in 0.611 seconds.