The generator matrix

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

generates a code of length 44 over Z4 who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+62x^33+177x^34+312x^35+451x^36+522x^37+628x^38+810x^39+900x^40+1124x^41+1222x^42+1216x^43+1357x^44+1312x^45+1292x^46+1178x^47+1009x^48+808x^49+601x^50+494x^51+335x^52+252x^53+168x^54+84x^55+42x^56+14x^57+8x^58+2x^59+2x^61+1x^76

The gray image is a code over GF(2) with n=88, k=14 and d=33.
This code was found by Heurico 1.10 in 8.16 seconds.