The generator matrix

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

generates a code of length 38 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+68x^28+94x^29+194x^30+278x^31+379x^32+478x^33+730x^34+988x^35+1531x^36+2246x^37+2338x^38+2194x^39+1657x^40+1134x^41+655x^42+438x^43+391x^44+260x^45+158x^46+64x^47+63x^48+12x^49+19x^50+6x^51+6x^52+1x^54+1x^62

The gray image is a code over GF(2) with n=152, k=14 and d=56.
This code was found by Heurico 1.16 in 9.12 seconds.