The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1 2a+2  1 2a+2  1  1  1  0  1  1  1  0  1  1  1  1 2a+2  1  0  1  1  1  2  2  1  1  1  1  1  0  1  1  2  0  2  1  0  1 2a+2  1  1
 0  1  0  0  0 2a+2  1 3a+2 3a+3 2a+3 2a+3  a 3a+2 3a+3  1 a+1  1  1 a+1  a  1 2a 3a+2 3a+1  1 2a+2 3a+1  a  3  1 3a+1 2a+2 2a  a 3a+3  1  1 3a+3 2a+3  1  1 2a+1  1 2a  0  1  1 2a+2 a+2  1 a+2  1 3a+3 2a+3
 0  0  1  1  a 3a+3  1  3  1  a  0  2 3a+3 a+3 3a+3 3a  3 3a+3  0 a+2  a 3a+1  3  2 2a+1 3a 2a+1 3a  3 3a+2 a+3  1  3 3a+3 a+2 a+3  0 a+3 3a+2 2a  2 a+3  0  a 3a+3 a+1 3a+2  1 2a+2 2a+2 a+3 a+2 a+3 2a+2
 0  0  0 2a+2  0  0  0  2  2  2 2a+2 2a 2a+2 2a 2a+2 2a 2a  2 2a+2 2a  2  2  0  0 2a 2a 2a+2  0 2a 2a+2 2a+2 2a+2 2a 2a+2  0  2 2a+2  0 2a+2 2a+2 2a 2a+2  2 2a+2  0  0 2a 2a  2  0  2 2a  2 2a
 0  0  0  0  2 2a+2 2a  2 2a+2 2a 2a  2  2 2a 2a  0  2 2a+2  2 2a  0  2  0  2 2a 2a+2 2a+2 2a+2 2a+2  0 2a  2  0  0 2a 2a  0 2a+2  2 2a+2 2a  2  2 2a+2  0  2  2  2 2a 2a+2 2a+2 2a+2  2  2

generates a code of length 54 over GR(16,4) who´s minimum homogenous weight is 146.

Homogenous weight enumerator: w(x)=1x^0+228x^146+516x^147+243x^148+336x^149+1164x^150+2088x^151+804x^152+852x^153+2640x^154+3816x^155+993x^156+1524x^157+3684x^158+4956x^159+1377x^160+2184x^161+5076x^162+6756x^163+1755x^164+2424x^165+4980x^166+5616x^167+1263x^168+1572x^169+2856x^170+3312x^171+537x^172+324x^173+828x^174+588x^175+81x^176+48x^178+42x^180+24x^184+21x^188+15x^192+6x^196+3x^200+3x^204

The gray image is a code over GF(4) with n=216, k=8 and d=146.
This code was found by Heurico 1.16 in 66 seconds.