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

generates a code of length 86 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+175x^72+2x^74+330x^76+70x^78+455x^80+268x^82+512x^83+592x^84+1536x^85+348x^86+1536x^87+631x^88+512x^89+266x^90+416x^92+62x^94+269x^96+8x^98+120x^100+64x^104+14x^108+3x^112+1x^120+1x^136

The gray image is a code over GF(2) with n=344, k=13 and d=144.
This code was found by Heurico 1.16 in 11.4 seconds.