The generator matrix

 1  0  0  1  1  1  X  1  1  1  1  1  1
 0  1  0  1  0 X+3  1  0  X X+2 X+2 X+1 X+3
 0  0  1  1  1  0  1  0  1 X+1  X X+1  1
 0  0  0  X  0 X+2  2  X  0  X  0 X+2  X
 0  0  0  0  X  0  2 X+2  0  X X+2  X  X
 0  0  0  0  0  2  2  0  2  2  0  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+139x^8+344x^9+596x^10+2720x^11+1288x^12+6160x^13+1352x^14+2720x^15+603x^16+344x^17+100x^18+16x^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 0.717 seconds.