The generator matrix

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

generates a code of length 67 over Z4 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+66x^54+122x^55+256x^56+392x^57+428x^58+482x^59+643x^60+706x^61+750x^62+910x^63+910x^64+960x^65+1028x^66+1032x^67+1051x^68+992x^69+952x^70+946x^71+776x^72+724x^73+622x^74+462x^75+363x^76+254x^77+220x^78+134x^79+89x^80+68x^81+25x^82+8x^83+7x^84+4x^86+1x^114

The gray image is a code over GF(2) with n=134, k=14 and d=54.
This code was found by Heurico 1.16 in 73.2 seconds.