The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1  1
 0  2  0  0  0  0  0  0  0  0  2  0  2
 0  0  2  0  0  0  0  0  0  0  2  2  0
 0  0  0  2  0  0  0  0  0  2  0  2  2
 0  0  0  0  2  0  0  0  0  2  0  0  2
 0  0  0  0  0  2  0  0  0  2  0  2  0
 0  0  0  0  0  0  2  0  0  2  2  2  2
 0  0  0  0  0  0  0  2  0  2  2  0  0
 0  0  0  0  0  0  0  0  2  2  2  0  2

generates a code of length 13 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+22x^6+55x^8+72x^10+352x^12+1024x^13+372x^14+87x^16+40x^18+16x^20+6x^22+1x^24

The gray image is a code over GF(2) with n=52, k=11 and d=12.
This code was found by Heurico 1.16 in 0.00886 seconds.