The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+38x^28+64x^29+16x^30+7x^32+2x^44

The gray image is a code over GF(2) with n=116, k=7 and d=56.
This code was found by Heurico 1.16 in 0.0861 seconds.