The generator matrix

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

generates a code of length 29 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+48x^21+111x^22+218x^23+281x^24+428x^25+600x^26+828x^27+1065x^28+1036x^29+1030x^30+832x^31+641x^32+484x^33+277x^34+164x^35+54x^36+52x^37+27x^38+6x^39+5x^40+2x^42+1x^44+1x^50

The gray image is a code over GF(2) with n=116, k=13 and d=42.
This code was found by Heurico 1.16 in 2.03 seconds.