The generator matrix

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

generates a code of length 44 over Z4 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+115x^32+186x^33+358x^34+556x^35+741x^36+976x^37+1287x^38+1500x^39+1929x^40+2046x^41+2362x^42+2756x^43+2672x^44+2906x^45+2541x^46+2348x^47+1964x^48+1650x^49+1290x^50+856x^51+653x^52+368x^53+313x^54+168x^55+101x^56+54x^57+38x^58+8x^59+14x^60+6x^61+3x^62+2x^64

The gray image is a code over GF(2) with n=88, k=15 and d=32.
This code was found by Heurico 1.16 in 76.1 seconds.