The generator matrix

 1  0  0  0  1  1  1  X  1  1  X  1  1
 0  1  0  0  1  2 X+1  1  0  X  1 X+3  1
 0  0  1  0  1  3  X X+1 X+1 X+1  3  3  0
 0  0  0  1  2  1 X+1 X+1  X  1  3 X+1  X

generates a code of length 13 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+80x^9+240x^10+580x^11+697x^12+876x^13+768x^14+548x^15+205x^16+84x^17+8x^18+8x^19+1x^20

The gray image is a code over GF(2) with n=52, k=12 and d=18.
This code was found by Heurico 1.11 in 0.0292 seconds.