The generator matrix

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

generates a code of length 13 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+126x^11+84x^12+148x^13+16x^14+96x^15+27x^16+12x^17+2x^19

The gray image is a code over GF(2) with n=52, k=9 and d=22.
This code was found by Heurico 1.16 in 0.0048 seconds.