The generator matrix

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

generates a code of length 35 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+198x^27+528x^28+1600x^29+1933x^30+4010x^31+4499x^32+7466x^33+7214x^34+10038x^35+7651x^36+8010x^37+4496x^38+3902x^39+1850x^40+1326x^41+418x^42+284x^43+60x^44+30x^45+19x^46+2x^48+1x^52

The gray image is a code over GF(2) with n=140, k=16 and d=54.
This code was found by Heurico 1.13 in 26.4 seconds.