The generator matrix

 1  0  0  0  1  1  1  2  1  1  1  1  1
 0  1  0  0  0  1 X+3  1  X  3  3 X+2  2
 0  0  1  0  1  1  X X+1 X+1  X  1  0  0
 0  0  0  1  1  0 X+1  1 X+2  X  1 X+1  X
 0  0  0  0  2  0  0  0  0  2  2  2  2
 0  0  0  0  0  2  0  2  0  0  2  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+95x^8+320x^9+890x^10+1960x^11+3097x^12+3648x^13+3126x^14+1936x^15+900x^16+320x^17+78x^18+8x^19+3x^20+2x^22

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 0.646 seconds.