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.