The generator matrix

 1  0  0  0  0  1  1  1  2  0  1  1  2  1  0  1  2  1  2  0  1  1  2  1  1  2  1  1  2  1  1  0  2  2  1  2  1  2
 0  1  0  0  0  0  0  0  0  0  0  2  1  3  1  1  2  1  1  1  1  3  2  1  2  0  3  3  1  2  0  1  2  1  3  1  3  0
 0  0  1  0  0  0  1  1  1  2  2  1  1  3  2  2  1  2  0  1  2  2  1  1  3  0  3  0  2  0  1  3  0  0  3  0  3  1
 0  0  0  1  0  1  1  0  3  2  0  0  0  0  0  2  2  2  3  3  1  3  1  3  3  1  2  3  2  2  3  2  1  3  0  2  2  1
 0  0  0  0  1  1  2  3  1  1  1  0  2  0  3  1  1  2  0  0  3  2  0  3  0  3  1  3  0  0  0  3  2  2  2  1  3  1
 0  0  0  0  0  2  0  2  2  2  0  2  2  2  2  2  2  0  2  2  2  0  2  0  0  0  2  0  2  2  2  2  2  0  0  2  0  2

generates a code of length 38 over Z4 who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+78x^31+166x^32+144x^33+87x^34+140x^35+228x^36+162x^37+80x^38+158x^39+246x^40+146x^41+62x^42+106x^43+100x^44+54x^45+24x^46+28x^47+27x^48+6x^49+3x^50+2x^51

The gray image is a code over GF(2) with n=76, k=11 and d=31.
This code was found by Heurico 1.16 in 12.3 seconds.