The generator matrix

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

generates a code of length 34 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+196x^31+154x^32+190x^33+118x^34+112x^35+62x^36+60x^37+41x^38+52x^39+7x^40+22x^41+8x^43+1x^46

The gray image is a code over GF(2) with n=136, k=10 and d=62.
This code was found by Heurico 1.11 in 184 seconds.