The generator matrix

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

generates a code of length 86 over GR(16,4) who´s minimum homogenous weight is 243.

Homogenous weight enumerator: w(x)=1x^0+312x^243+165x^244+180x^245+180x^246+1020x^247+198x^248+312x^249+396x^250+1272x^251+150x^252+612x^253+540x^254+1596x^255+129x^256+540x^257+648x^258+1500x^259+87x^260+588x^261+828x^262+1680x^263+66x^264+576x^265+396x^266+1200x^267+42x^268+252x^269+84x^270+492x^271+42x^272+12x^273+132x^275+27x^276+12x^279+24x^280+21x^284+27x^288+27x^292+6x^296+3x^300+3x^304+6x^316

The gray image is a code over GF(4) with n=344, k=7 and d=243.
This code was found by Heurico 1.16 in 80.5 seconds.