The generator matrix

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

generates a code of length 38 over Z4 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+89x^32+215x^34+192x^36+125x^38+142x^40+105x^42+84x^44+59x^46+4x^48+8x^50

The gray image is a code over GF(2) with n=76, k=10 and d=32.
This code was found by Heurico 1.16 in 0.0737 seconds.