The generator matrix

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

generates a code of length 34 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+49x^26+78x^27+230x^28+232x^29+556x^30+508x^31+1035x^32+732x^33+1355x^34+720x^35+1088x^36+500x^37+556x^38+212x^39+192x^40+68x^41+35x^42+18x^43+10x^44+4x^45+8x^46+4x^48+1x^50

The gray image is a code over GF(2) with n=136, k=13 and d=52.
This code was found by Heurico 1.16 in 1.5 seconds.