The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  2  2  1
 0  2  0  0  0  0  0  0  0  0  0  2  0  2  0  2  0  2  2  2  0  2  2  2  0  2  0  2  2  2  2  2  0  0  0  0  0  0  2  2  2  2  0  0
 0  0  2  0  0  0  0  0  0  0  2  0  2  0  2  0  2  2  2  0  2  2  2  0  2  2  2  2  2  2  0  0  0  0  0  0  2  2  2  2  2  0  2  0
 0  0  0  2  0  0  0  2  2  2  2  2  2  2  0  0  2  0  0  2  2  2  2  2  0  0  0  0  2  2  0  0  0  0  0  2  2  0  0  0  2  2  0  0
 0  0  0  0  2  0  2  2  2  0  0  0  0  0  0  0  2  0  2  2  2  2  0  2  2  0  2  2  2  0  2  2  0  0  2  2  0  0  0  2  2  0  0  0
 0  0  0  0  0  2  2  0  2  2  0  0  2  2  2  2  2  0  2  2  0  0  0  0  0  2  2  0  2  2  0  2  0  2  2  0  0  0  0  0  0  2  2  0

generates a code of length 44 over Z4 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+16x^40+8x^41+10x^42+24x^43+12x^44+24x^45+12x^46+8x^47+3x^48+9x^50+1x^82

The gray image is a code over GF(2) with n=88, k=7 and d=40.
This code was found by Heurico 1.16 in 0.0124 seconds.