The generator matrix

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

generates a code of length 14 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+50x^10+174x^11+490x^12+794x^13+1092x^14+784x^15+495x^16+160x^17+42x^18+2x^19+6x^20+6x^21

The gray image is a code over GF(2) with n=112, k=12 and d=40.
This code was found by Heurico 1.16 in 0.047 seconds.