The generator matrix

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

generates a code of length 67 over Z4 who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+22x^55+114x^56+170x^57+230x^58+282x^59+380x^60+388x^61+395x^62+542x^63+495x^64+478x^65+446x^66+428x^67+459x^68+510x^69+456x^70+440x^71+466x^72+304x^73+287x^74+272x^75+218x^76+162x^77+91x^78+60x^79+36x^80+32x^81+12x^82+2x^83+7x^84+4x^85+2x^86+1x^90

The gray image is a code over GF(2) with n=134, k=13 and d=55.
This code was found by Heurico 1.10 in 3.82 seconds.