The generator matrix

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

generates a code of length 35 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+35x^26+82x^27+184x^28+414x^29+449x^30+1084x^31+921x^32+2062x^33+1462x^34+2838x^35+1524x^36+2298x^37+951x^38+1018x^39+393x^40+330x^41+159x^42+96x^43+44x^44+16x^45+15x^46+2x^47+4x^48+1x^54+1x^56

The gray image is a code over GF(2) with n=140, k=14 and d=52.
This code was found by Heurico 1.16 in 5.78 seconds.