The generator matrix

 1  1  1  1  1  1  1  1  1  X  X 2X+2  1  X
 0  2  0 2X+2  0  0 2X+2  2 2X 2X 2X+2 2X 2X  2
 0  0  2 2X+2  0  2  2 2X 2X 2X+2 2X+2 2X+2 2X+2  0
 0  0  0 2X  0  0 2X  0  0 2X  0  0 2X 2X
 0  0  0  0 2X  0  0 2X  0 2X  0 2X  0 2X
 0  0  0  0  0 2X 2X  0 2X  0  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+62x^10+16x^11+198x^12+368x^13+774x^14+368x^15+175x^16+16x^17+58x^18+10x^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 0.312 seconds.