The generator matrix

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

generates a code of length 34 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+26x^24+36x^25+97x^26+114x^27+205x^28+264x^29+436x^30+628x^31+782x^32+988x^33+984x^34+1000x^35+822x^36+676x^37+449x^38+268x^39+176x^40+80x^41+69x^42+38x^43+29x^44+4x^45+10x^46+7x^48+2x^50+1x^54

The gray image is a code over GF(2) with n=136, k=13 and d=48.
This code was found by Heurico 1.16 in 2.08 seconds.