The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 2X  1  1  1  0  1  1 2X+2  1  X  1
 0  X  0  X 2X  0 3X  X  2 X+2  2 X+2 2X+2  2 3X+2 X+2  0 2X  X 2X+2 2X  0  X 2X+2 2X+2  X  X 3X+2  0
 0  0  X  X  2 X+2 X+2  2  2 3X+2  X 2X  0 X+2 3X 2X+2 2X 3X+2  2  2 3X 2X+2 X+2  X X+2 3X+2 3X  2  0

generates a code of length 29 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+51x^26+164x^27+210x^28+216x^29+198x^30+112x^31+44x^32+8x^33+6x^34+12x^35+1x^40+1x^50

The gray image is a code over GF(2) with n=232, k=10 and d=104.
This code was found by Heurico 1.16 in 0.015 seconds.