The generator matrix

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

generates a code of length 44 over Z4 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+60x^30+146x^31+303x^32+460x^33+728x^34+896x^35+1456x^36+1906x^37+2496x^38+3166x^39+3705x^40+4378x^41+4714x^42+5314x^43+5346x^44+5408x^45+5170x^46+4638x^47+3938x^48+3146x^49+2501x^50+1844x^51+1392x^52+946x^53+648x^54+354x^55+221x^56+126x^57+64x^58+26x^59+22x^60+12x^61+2x^62+2x^65+1x^66

The gray image is a code over GF(2) with n=88, k=16 and d=30.
This code was found by Heurico 1.10 in 113 seconds.