The generator matrix

 1  0  0  0  1  1  1  2  0  1 X+2  1  1
 0  1  0  0  0  3 X+1  1  1  3  1  1  0
 0  0  1  0  1  1  X X+1  X X+1  0  3  0
 0  0  0  1  1  X  1  1 X+3  X X+1 X+2  2
 0  0  0  0  X  0  0  2  X X+2  2  X  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+128x^8+316x^9+885x^10+1816x^11+3064x^12+3896x^13+3111x^14+1904x^15+891x^16+236x^17+99x^18+24x^19+12x^20+1x^22

The gray image is a code over GF(2) with n=52, k=14 and d=16.
This code was found by Heurico 1.13 in 0.309 seconds.