The generator matrix

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

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+50x^10+32x^11+194x^12+480x^13+542x^14+480x^15+183x^16+32x^17+46x^18+6x^20+2x^22

The gray image is a code over GF(2) with n=112, k=11 and d=40.
This code was found by Heurico 1.16 in 0.016 seconds.