The generator matrix

 1  0  1  1  1  0  1  1  2  1  1  1  1
 0  1  1  0  1  1  0 X+1  1  X X+2 X+1  1
 0  0  X  0  0  0 X+2  X  X  X  2  0 X+2
 0  0  0  X  0  0  0  X X+2  X X+2  X  2
 0  0  0  0  X X+2  0  2  X  X  X X+2  0
 0  0  0  0  0  2  0  2  2  0  0  0  2
 0  0  0  0  0  0  2  0  0  2  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+319x^8+32x^9+1056x^10+1152x^11+3800x^12+3776x^13+3584x^14+1152x^15+1231x^16+32x^17+224x^18+24x^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 10.8 seconds.