The generator matrix

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

generates a code of length 64 over Z4 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+53x^54+108x^55+165x^56+202x^57+240x^58+242x^59+267x^60+276x^61+234x^62+244x^63+220x^64+242x^65+211x^66+224x^67+225x^68+202x^69+187x^70+132x^71+105x^72+84x^73+76x^74+70x^75+35x^76+18x^77+22x^78+4x^79+5x^80+1x^82+1x^84

The gray image is a code over GF(2) with n=128, k=12 and d=54.
This code was found by Heurico 1.16 in 2.23 seconds.