The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+39x^10+186x^11+375x^12+782x^13+1358x^14+768x^15+353x^16+176x^17+43x^18+6x^19+7x^20+2x^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 0.031 seconds.