The generator matrix

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

generates a code of length 35 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+247x^28+156x^29+766x^30+620x^31+1678x^32+1372x^33+2416x^34+1836x^35+2523x^36+1396x^37+1612x^38+612x^39+738x^40+148x^41+192x^42+4x^43+53x^44+6x^46+7x^48+1x^52

The gray image is a code over GF(2) with n=140, k=14 and d=56.
This code was found by Heurico 1.16 in 79.3 seconds.