The generator matrix

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

generates a code of length 29 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+63x^28+54x^30+7x^32+2x^34+1x^36

The gray image is a code over GF(2) with n=232, k=7 and d=112.
This code was found by Heurico 1.16 in 0.016 seconds.