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  X  0  1  1  X  0  X  0  1  1  1  X  1  0  X  0  1  1  1  1  1  1  1  0  1  X  1  1  1  1  1  1  0  X  2  1  0  X  1  2  0  X  1  0  1  1  1  2  1  1  X  2  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  0 X+2  X  2  2 X+2  X  X  X X+2  X X+2  X X+2 X+2  0 X+2  2  X X+2  X  2 X+2 X+2 X+2  X  2 X+2  X  0 X+2  0 X+2  X  X X+2  2  X  2  X  0  X  X  2  0  X X+2 X+2  X  X  X X+2  X  2  0 X+2  0  0  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  2  0  2  2  0  0  2  0  0  0  2  2  0  2  0  0  2  0  0  2  0  0  0  2  0  0  0  2  2  2  2  0  0  2  2  2  0  0  0  0  0  2  2  2  2  2  0  0  0  2  0  2  2  0  2  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  0  2  0  0  0  0  2  0  2  2  2  2  2  2  2  0  2  0  0  0  2  2  2  0  0  0  2  2  2  2  0  0  2  0  0  0  0  2  2  2  0  0  2  2  2  0  2  0  0  2  2  2  2  0  0  2  2  2  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  2  0  0  2  2  2  2  0  0  2  0  2  0  0  2  0  0  2  2  2  0  0  0  2  2  2  0  0  2  2  0  0  2  0  2  2  0  2  0  2  2  0  2  0  2  2  0  2  0  0  2  0  2  0  2  0  2  0  2  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  0  2  2  0  2  2  2  0  2  2  2  0  2  0  2  2  0  2  2  2  2  2  0  2  2  2  0  2  0  0  2  0  0  2  0  2  2  2  2  2  0  2  0  0  2  0  0  0  0  2  0  0  2  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  0  0  0  0  2  2  0  0  0  0  0  0  2  2  2  0  2  0  0  0  2  2  2  0  0  0  2  2  2  2  2  2  2  2  0  2  2  2  0  2  2  0  0  0  2  0  2  2  0  0  2  2  0  0  2  0  0  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  2  0  0  2  0  0  0  0  2  2  2  0  2  0  2  2  0  0  2  2  2  0  0  2  2  0  2  0  0  0  2  0  2  0  0  2  2  2  0  2  0  0  2  2  0  2  2  0  0  0  2  2  0  2  2  2  2  0  2  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  0  0  0  2  0  2  0  2  0  2  2  2  0  2  0  0  2  2  2  0  2  2  2  2  0  2  0  0  0  0  0  0  2  0  0  0  0  2  2  0  2  2  0  2  2  0  0  2  0  0  2  2  0  2  0  0  2  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  2  0  0  0  2  0  2  0  0  0  2  2  0  2  0  2  0  2  0  2  2  0  2  0  0  0  2  0  2  0  2  2  2  0  2  2  2  2  0  0  0  0  0  2  2  2  2  0  0  0  0  0  0  2  0  2  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+68x^72+18x^73+85x^74+80x^75+189x^76+156x^77+224x^78+356x^79+370x^80+514x^81+507x^82+568x^83+611x^84+680x^85+693x^86+632x^87+526x^88+502x^89+297x^90+336x^91+196x^92+156x^93+143x^94+68x^95+54x^96+22x^97+55x^98+8x^99+23x^100+24x^102+4x^104+15x^106+5x^108+3x^110+1x^112+1x^118+1x^122

The gray image is a code over GF(2) with n=340, k=13 and d=144.
This code was found by Heurico 1.16 in 9.13 seconds.