The generator matrix

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

generates a code of length 14 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+225x^8+804x^9+2895x^10+7586x^11+15579x^12+24296x^13+28091x^14+24574x^15+15666x^16+7460x^17+2861x^18+798x^19+209x^20+16x^21+9x^22+2x^23

The gray image is a code over GF(2) with n=56, k=17 and d=16.
This code was found by Heurico 1.13 in 12 seconds.