The generator matrix

 1  0  1  1  1  0  1  1  X  X  1  1  X
 0  1  1  0 X+1  1  X X+3  1  2  2 X+2  0
 0  0  X X+2  0 X+2  X  X X+2  X  X  0  0
 0  0  0  2  0  0  0  2  2  0  2  0  0
 0  0  0  0  2  0  0  0  0  2  2  0  2
 0  0  0  0  0  2  0  0  2  2  2  0  0
 0  0  0  0  0  0  2  2  2  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+85x^8+32x^9+264x^10+384x^11+942x^12+704x^13+896x^14+384x^15+305x^16+32x^17+56x^18+10x^20+1x^24

The gray image is a code over GF(2) with n=52, k=12 and d=16.
This code was found by Heurico 1.16 in 0.0377 seconds.