The generator matrix

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

generates a code of length 52 over GR(16,4) who´s minimum homogenous weight is 138.

Homogenous weight enumerator: w(x)=1x^0+444x^138+696x^139+972x^140+756x^141+2928x^142+2628x^143+3564x^144+2184x^145+7512x^146+5604x^147+6891x^148+4512x^149+13716x^150+10140x^151+11766x^152+7488x^153+21732x^154+13344x^155+16218x^156+9804x^157+24984x^158+14844x^159+14991x^160+8136x^161+18480x^162+10404x^163+8712x^164+3240x^165+7524x^166+3396x^167+2136x^168+720x^169+984x^170+384x^171+198x^172+24x^173+30x^176+21x^180+18x^184+12x^188+6x^192

The gray image is a code over GF(4) with n=208, k=9 and d=138.
This code was found by Heurico 1.16 in 295 seconds.