The generator matrix

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

generates a code of length 66 over Z4 who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+92x^55+186x^56+260x^57+313x^58+382x^59+389x^60+380x^61+498x^62+424x^63+428x^64+550x^65+481x^66+484x^67+490x^68+464x^69+455x^70+396x^71+393x^72+322x^73+222x^74+162x^75+140x^76+114x^77+75x^78+40x^79+20x^80+20x^81+4x^82+4x^83+2x^85+1x^100

The gray image is a code over GF(2) with n=132, k=13 and d=55.
This code was found by Heurico 1.16 in 75.8 seconds.