The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  1 X+2  1  1  0  1  1  1  0  1 X+2  1  1  0  1 X+2  1  1  1  1  0  1  1  1 X+2  1  0  1  1 X+2  1  1  1 X+2  1  X  1  1  0 X+2  1  1  0  1  1  1  1  1  1  2  1 X+2  1  1  X  2  X  1  1  1 X+2  X  1  X  X  1  1  0  1  1  1  1  1
 0  1 X+1 X+2  1  1  0 X+1  1 X+2  3  1 X+2  1 X+1  0  1  3  3  0  1 X+2  1 X+1 X+3  1 X+2  1  3  0 X+1  0  1 X+2  3  0  1 X+1  1 X+1  0  1  3 X+2  3  1 X+1  1 X+1  3  1  1 X+2  3  1  X X+3 X+1  1  2  2  1 X+2  1  3  0  1  1  1  0  X X+1  1  1  0 X+2  2 X+3  0  1 X+1 X+3 X+1  0  0
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  0  2  0  0  2  2  0  0  2  0  2  0  2  2  0  2  2  0  2  0  2  2  0  0  0  0  2  2  2  2  0  2  2  2  0  2  0  0  0  0  2  0  2  0  2  0  0  0  2  2  2  0  0  2  2  0  0  2  2  2  2  2  2  0  2  2  0  0  0  0
 0  0  0  2  0  0  0  0  0  0  0  0  2  0  0  2  2  2  2  2  2  2  0  2  2  0  2  0  2  0  2  2  0  0  2  0  2  0  2  0  2  2  0  0  0  2  2  0  0  0  2  0  0  2  2  2  0  2  0  0  0  0  2  2  0  2  2  2  0  0  2  0  2  2  2  0  0  0  0  0  0  2  2  0  0
 0  0  0  0  2  0  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  2  2  2  2  2  2  0  0  2  2  2  2  2  2  2  2  2  0  2  2  2  2  2  0  2  0  0  2  0  0  0  0  2  2  0  2  0  0  2  2  0  0  2  0  0  2  0  0  0  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  2  0  2  2  2  2  0  0  0  2  2  2  2  0  2  2  0  2  0  0  0  0  0  0  2  2  2  0  2  0  2  2  0  0  2  0  2  0  0  0  2  0  2  2  0  0  2  2  0  0  2  2  2  2  2  0  2  0  2  0  2  0  2  2  2  2  2  0  2  0  0  0
 0  0  0  0  0  0  2  0  0  0  2  0  2  0  2  0  2  2  0  0  2  2  2  2  0  2  2  2  0  2  2  2  2  2  2  0  0  0  2  2  2  0  0  0  0  2  0  2  0  0  0  2  2  2  0  2  0  0  2  2  0  0  0  0  0  2  0  0  2  0  2  0  0  0  0  0  0  0  2  2  2  0  0  0  0
 0  0  0  0  0  0  0  2  0  0  0  2  0  2  2  0  0  2  2  2  0  0  2  0  0  2  0  2  0  0  2  2  2  0  2  0  2  0  2  2  0  2  2  2  0  0  0  2  2  0  0  0  2  2  2  2  0  2  2  0  0  0  2  0  2  0  0  0  0  0  2  0  2  2  0  2  0  0  0  0  2  0  2  2  2
 0  0  0  0  0  0  0  0  2  0  2  2  0  2  2  2  2  2  0  0  0  2  0  0  2  0  2  2  2  0  0  0  2  0  2  2  2  2  2  0  2  2  2  2  0  0  2  2  0  0  0  2  0  0  2  2  2  0  2  2  0  0  0  2  0  2  2  0  2  0  2  2  0  2  2  0  2  2  0  2  2  0  2  0  0
 0  0  0  0  0  0  0  0  0  2  2  0  2  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  2  0  2  0  0  0  2  0  0  0  2  0  2  0  2  2  0  0  0  2  2  2  0  2  0  0  0  0  2  2  2  0  2  2  0  0  2  2  2  0  2  2  0  0  2  2  0  0  2  0  0  2  0  0  0  0  0

generates a code of length 85 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+91x^72+80x^74+28x^75+426x^76+152x^77+616x^78+412x^79+1021x^80+720x^81+1214x^82+1064x^83+1736x^84+1344x^85+1592x^86+1160x^87+1438x^88+688x^89+836x^90+380x^91+653x^92+168x^93+240x^94+28x^95+164x^96+30x^98+58x^100+33x^104+7x^108+4x^112

The gray image is a code over GF(2) with n=340, k=14 and d=144.
This code was found by Heurico 1.16 in 22.2 seconds.