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

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+66x^72+26x^74+296x^76+276x^78+708x^80+806x^82+1278x^84+1368x^86+1258x^88+806x^90+647x^92+276x^94+233x^96+26x^98+68x^100+32x^104+12x^108+6x^112+2x^116+1x^124

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 9.23 seconds.