The generator matrix

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

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+48x^8+16x^9+286x^10+528x^11+814x^12+1504x^13+1774x^14+1504x^15+879x^16+528x^17+234x^18+16x^19+50x^20+10x^22

The gray image is a code over GF(2) with n=56, k=13 and d=16.
This code was found by Heurico 1.16 in 0.15 seconds.