The generator matrix

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

generates a code of length 66 over Z4 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+50x^54+70x^55+210x^56+236x^57+289x^58+384x^59+359x^60+442x^61+480x^62+450x^63+468x^64+468x^65+465x^66+498x^67+439x^68+506x^69+412x^70+424x^71+374x^72+282x^73+267x^74+178x^75+159x^76+100x^77+82x^78+40x^79+35x^80+14x^81+2x^82+4x^83+3x^84+1x^98

The gray image is a code over GF(2) with n=132, k=13 and d=54.
This code was found by Heurico 1.10 in 3.71 seconds.