The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  1  1  X  0  1  X  0  1  X  0  1  1  1  1  X  0  X  1  1  1  0  1  1  1  1  1  X  1  1  0  1  X  1  1  1  1  1  1  0  X  1  X  1  1  1  X  0  1  1  1  1  1  1  1
 0  X  0 X+2  0 X+2  0 X+2  0 X+2  2 X+2  0 X+2  0 X+2  X  2 X+2  0  2 X+2  2  X  0 X+2  X X+2  X  0 X+2  X  0 X+2  X  X X+2  X X+2  0 X+2  X X+2  X X+2  X  2  0  X X+2  X  2  2  X X+2  0 X+2  X  X X+2  X X+2  2  X  X  X  X X+2  X  X  2  2  X  X  2  2  0 X+2 X+2  0  0  0
 0  0  2  0  0  0  0  0  0  0  2  0  2  0  0  0  0  2  2  2  2  2  0  2  0  0  2  0  0  2  0  0  2  2  0  2  2  2  0  2  2  2  2  0  0  0  2  0  0  2  0  2  0  0  0  2  0  0  2  2  0  2  0  2  2  0  0  2  0  2  2  0  0  2  0  0  0  2  2  2  0  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  2  0  0  2  0  2  0  0  2  0  2  0  0  0  0  2  0  0  2  0  2  0  2  2  0  2  2  0  0  2  0  2  2  2  2  0  2  0  2  0  2  0  2  0  2  0  0  2  2  2  2  2  2  0  0  0  2  0  2  0  2  0  0  2  2  0  0  0  0
 0  0  0  0  2  0  0  0  0  0  0  0  2  0  0  0  0  2  0  0  0  0  2  0  2  2  2  0  0  2  0  2  2  0  0  0  2  2  2  2  2  2  2  2  0  2  0  0  2  0  2  2  0  2  0  0  2  0  0  2  2  0  0  0  2  2  2  2  0  2  2  0  2  2  2  2  2  2  0  0  0  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  2  0  2  0  0  0  0  0  0  0  2  2  0  2  2  2  2  2  2  2  2  2  2  0  0  0  2  0  2  0  2  2  2  0  2  0  0  0  0  2  0  2  0  2  0  0  0  2  0  2  2  2  0  0  2  2  2  2  2  2  0  2  2  0  0  0  0  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  2  0  2  0  0  0  0  2  2  0  2  0  2  2  2  2  2  0  2  0  2  0  2  2  2  0  0  0  2  0  0  0  0  0  2  0  2  2  2  2  0  2  2  0  2  2  0  2  0  2  0  2  2  0  0  0  2  0  2  2  2  0  0  2  0  0  2  0  0  0
 0  0  0  0  0  0  0  2  0  0  0  2  0  0  2  2  0  2  2  0  2  2  0  0  2  0  2  2  0  0  2  0  0  2  0  2  2  0  2  2  0  0  0  2  2  2  2  2  2  2  2  0  2  0  0  2  2  0  0  2  2  2  2  0  2  2  2  2  2  2  0  2  0  0  2  0  0  2  2  0  0  0
 0  0  0  0  0  0  0  0  2  0  2  0  2  0  2  2  2  0  2  0  2  0  0  2  0  2  2  2  2  2  0  2  0  2  2  2  0  2  2  2  2  2  0  0  0  2  2  2  2  0  0  2  2  2  2  2  2  2  0  0  0  2  0  2  0  2  2  2  0  0  0  0  2  0  0  0  2  2  0  0  0  0
 0  0  0  0  0  0  0  0  0  2  0  2  0  0  2  0  2  2  2  2  0  0  2  2  0  2  0  0  0  0  2  0  2  0  0  2  0  2  2  0  0  2  2  0  0  2  2  2  2  2  0  0  0  2  2  2  2  0  0  2  2  0  2  2  2  0  0  2  0  0  0  2  0  0  0  0  0  0  2  0  0  0

generates a code of length 82 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+73x^68+36x^70+257x^72+4x^73+220x^74+36x^75+579x^76+144x^77+620x^78+336x^79+934x^80+504x^81+826x^82+504x^83+917x^84+336x^85+596x^86+144x^87+474x^88+36x^89+216x^90+4x^91+219x^92+44x^94+78x^96+2x^98+32x^100+15x^104+3x^108+1x^112+1x^124

The gray image is a code over GF(2) with n=328, k=13 and d=136.
This code was found by Heurico 1.16 in 8.71 seconds.