The generator matrix

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

generates a code of length 44 over Z4 who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+49x^38+102x^40+86x^42+79x^44+79x^46+44x^48+32x^50+24x^52+7x^54+4x^56+2x^58+1x^60+1x^62+1x^64

The gray image is a code over GF(2) with n=88, k=9 and d=38.
This code was found by Heurico 1.16 in 0.0381 seconds.