The generator matrix

 1  1  1  1  X  1  1  0  X  1  1  X  1  1
 0  X  0 X+2  X  0 X+2  X  X  0 X+2 X+2 X+2 X+2
 0  0  2  0  0  0  0  0  0  0  0  2  2  2
 0  0  0  2  0  0  0  0  0  0  2  2  2  0
 0  0  0  0  2  0  0  0  0  2  2  0  0  2
 0  0  0  0  0  2  0  0  0  2  0  0  2  2
 0  0  0  0  0  0  2  0  0  0  2  0  2  2
 0  0  0  0  0  0  0  2  0  2  2  0  2  0
 0  0  0  0  0  0  0  0  2  2  0  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+85x^8+112x^10+128x^11+544x^12+896x^13+544x^14+896x^15+579x^16+128x^17+112x^18+64x^20+7x^24

The gray image is a code over GF(2) with n=56, k=12 and d=16.
This code was found by Heurico 1.16 in 0.0404 seconds.