The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  2  2  2  2  1  2  0  1  1  2  2  2  1  0  2  1  1  1  2  1  1  1  0  0  2  2  1  1  1  0  0  2  2  1  1  2  0  2  2  1  0  0  0  2  2  0  1  1  1  1  2  0
 0  1  0  0  0  1  1  1  2  0  3  1  1  0  1  2  1  1  1  1  2  0  2  2  0  2  1  3  2  2  0  1  0  2  1  1  0  1  3  1  2  1  0  1  1  1  2  1  0  2  2  0  2  1  1  0  2  1  3  2  3  0  2  2
 0  0  1  0  1  1  0  1  0  3  3  2  0  1  2  1  0  1  3  2  1  1  2  1  1  1  1  1  0  0  1  1  3  2  2  3  1  3  2  3  0  3  0  2  0  3  0  1  2  2  1  2  1  3  0  1  0  3  2  3  2  3  0  2
 0  0  0  1  1  0  1  1  1  0  1  2  0  1  1  0  2  0  1  1  0  0  1  1  3  3  2  1  2  1  2  2  0  1  1  0  3  2  0  3  3  1  1  1  0  3  0  1  1  1  1  2  3  3  0  1  1  2  1  1  0  0  1  1
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  2  0  2  0  0  2  2  0  2  0  0  0  2  2  0  0  2  0  0  2  2  2  0  0  2  2  0  2  0  0  0  0  0  2  2  0  2  2  2  2  2  0  2
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  2  2  2  2  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  2  2  0
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  0  2  2  2  0  2  2  0  2  2  2  0  0  2  0  0  0  2  2  2  0  0  2  2  2  0  0  2  2  0  0  0  0  2  0  0  2  2  0  2  2  0  2  0  0  2  2  2  0  2
 0  0  0  0  0  0  0  2  2  2  0  0  2  2  2  0  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  2  0  2  2  2  2  2  2  2  2  2  0  0  2  0  2  0  2  0  0  0  0  2  2  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+84x^54+96x^55+150x^56+190x^57+225x^58+244x^59+256x^60+296x^61+234x^62+248x^63+243x^64+250x^65+206x^66+220x^67+208x^68+180x^69+178x^70+180x^71+116x^72+86x^73+79x^74+32x^75+38x^76+20x^77+16x^78+4x^79+10x^80+2x^81+2x^82+2x^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 2.38 seconds.