The generator matrix

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

generates a code of length 75 over Z4 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+73x^56+8x^58+291x^60+138x^62+745x^64+498x^66+1299x^68+1182x^70+2173x^72+1668x^74+2208x^76+1504x^78+1812x^80+826x^82+1002x^84+278x^86+434x^88+40x^90+153x^92+2x^94+38x^96+7x^100+3x^104+1x^120

The gray image is a code over GF(2) with n=150, k=14 and d=56.
This code was found by Heurico 1.16 in 55.4 seconds.