The generator matrix

 1  1  1  1  1  1  1  1  X  1  X  1  1
 0  X  0  0  0  0  0  2 X+2  X  2 X+2  0
 0  0  X  0  0  2 X+2  X X+2  X  X  0  0
 0  0  0  X  0 X+2 X+2  X  2 X+2 X+2  0  0
 0  0  0  0  X  X  2  X  X X+2  X  0  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+74x^8+32x^9+73x^10+216x^11+342x^12+528x^13+399x^14+224x^15+81x^16+16x^17+39x^18+8x^19+14x^20+1x^22

The gray image is a code over GF(2) with n=52, k=11 and d=16.
This code was found by Heurico 1.16 in 0.0208 seconds.