The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  X  1  X  X  X  X  X  X  1  1  1  1  X  1  1  1  1  X
 0 2X  0  0  0 2X 2X 2X  0  0  0 2X  0 2X 2X 2X  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X
 0  0 2X  0 2X 2X 2X  0  0  0 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X  0  0  0  0  0 2X 2X  0
 0  0  0 2X 2X  0 2X 2X  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0  0 2X 2X  0  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+18x^28+96x^29+6x^30+4x^32+2x^38+1x^40

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 6.87e-008 seconds.