The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  X  X 2X+2
 0  2  0  0  0 2X+2  2 2X+2  0 2X 2X 2X+2 2X+2  2
 0  0  2  0 2X+2 2X+2 2X+2 2X  0 2X  0 2X+2  2  0
 0  0  0  2 2X+2 2X  2  2  0  2 2X+2  0  0 2X
 0  0  0  0 2X 2X 2X 2X 2X 2X 2X 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+37x^10+82x^11+131x^12+432x^13+698x^14+436x^15+113x^16+64x^17+33x^18+10x^19+11x^20

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.