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

generates a code of length 85 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+153x^74+4x^75+276x^76+80x^77+370x^78+240x^79+434x^80+492x^81+443x^82+784x^83+466x^84+920x^85+439x^86+776x^87+398x^88+464x^89+348x^90+236x^91+292x^92+88x^93+200x^94+8x^95+136x^96+4x^97+75x^98+38x^100+11x^102+5x^104+5x^106+4x^110+1x^112+1x^120

The gray image is a code over GF(2) with n=340, k=13 and d=148.
This code was found by Heurico 1.16 in 32.3 seconds.