The generator matrix

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

generates a code of length 66 over Z4 who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+30x^51+89x^52+248x^53+334x^54+450x^55+633x^56+786x^57+992x^58+1120x^59+1299x^60+1538x^61+1709x^62+1852x^63+1966x^64+2080x^65+2140x^66+2148x^67+2167x^68+1974x^69+1835x^70+1626x^71+1353x^72+1200x^73+905x^74+648x^75+536x^76+394x^77+229x^78+168x^79+123x^80+92x^81+40x^82+22x^83+20x^84+6x^85+5x^86+4x^88+2x^89+3x^90+1x^92

The gray image is a code over GF(2) with n=132, k=15 and d=51.
This code was found by Heurico 1.10 in 51.8 seconds.