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

generates a code of length 84 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+142x^72+110x^74+4x^75+479x^76+36x^77+416x^78+144x^79+781x^80+336x^81+706x^82+504x^83+971x^84+504x^85+712x^86+336x^87+664x^88+144x^89+522x^90+36x^91+365x^92+4x^93+88x^94+101x^96+6x^98+54x^100+19x^104+2x^108+3x^112+1x^116+1x^120

The gray image is a code over GF(2) with n=336, k=13 and d=144.
This code was found by Heurico 1.16 in 10.2 seconds.