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  1 X+2  1  1  0  1 X+2  1  1  1  1  1  0  1 X+2  1  1  0  1  2 X+2  1  1  1 X+2  0  1  1  1  1  1  1 X+2  X  1  1 X+2  1  1  1  X  X  0  1  X  1  1  1  1  0  1  1 X+2  1 X+2 X+2  1  1  1  1  0  0  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  0  3  1 X+2 X+1  1 X+1  3  1  0  1 X+2  3  0 X+1 X+2  1  X  1  3  0  1  2  1  1 X+1 X+2  3  1  1 X+1  3 X+2  0 X+1 X+2  1  1  3 X+1  1  0  3  1  1  1  1  1  1  1  2  3  0  1  0  3  1  2  1  1  3 X+3  0 X+2  1  1  0  0
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  0  2  0  2  0  0  0  0  2  2  2  2  0  0  2  2  0  2  2  0  2  0  2  2  2  0  2  0  2  2  0  0  2  2  2  2  0  0  0  2  0  2  0  0  0  2  0  2  0  2  2  0  0  0  2  0  2  0  0  0  0  2  2  2  0  0  2  0  2  0  0
 0  0  0  2  0  0  0  0  0  0  0  0  2  0  0  2  2  2  2  2  0  2  0  2  2  0  2  0  0  0  0  0  2  2  2  0  2  2  0  2  2  0  2  2  0  0  2  0  2  0  2  0  0  2  2  0  0  0  0  2  0  0  2  2  0  2  2  2  2  2  2  0  0  0  2  2  0  0  2  2  0  0  0  0  0  0
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  0  2  2  2  2  2  2  0  0  0  0  2  2  2  2  2  0  2  0  2  2  2  2  0  0  2  0  0  0  0  0  0  2  0  0  2  0  2  0  2  0  0  2  2  2  2  2  0  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  2  0  2  2  2  0  2  2  0  2  2  2  2  0  2  2  2  0  0  2  2  0  2  2  0  0  0  2  2  0  2  2  0  2  2  0  0  0  0  2  2  2  2  2  2  2  0  0  0  2  2  2  2  2  0  2  2  2  0  2  0  0  0  2  0  0  0  0  2  0  0  0  0
 0  0  0  0  0  0  2  0  0  0  2  0  2  0  2  0  2  2  0  2  2  2  2  0  2  0  2  2  0  2  2  2  2  0  0  0  2  2  0  2  2  2  2  2  2  2  0  0  2  2  0  0  2  0  0  0  0  0  2  0  0  2  2  0  2  2  0  0  0  2  2  2  2  2  0  0  0  0  0  0  2  2  0  2  0  0
 0  0  0  0  0  0  0  2  0  0  0  2  0  2  2  0  0  2  2  0  0  2  2  0  2  0  0  0  2  2  2  0  2  2  0  2  0  0  0  2  0  0  2  2  2  2  0  2  2  0  0  0  0  2  0  2  0  0  2  0  2  0  0  2  2  0  2  0  0  2  2  0  2  2  0  2  2  0  0  2  2  2  2  2  0  0
 0  0  0  0  0  0  0  0  2  0  2  2  0  2  2  2  2  2  0  2  2  0  0  0  2  0  0  0  0  2  0  0  0  0  2  2  0  2  2  2  2  2  0  2  0  2  2  0  0  2  0  2  2  0  0  0  0  2  0  2  0  0  2  2  0  2  0  2  2  0  0  2  0  0  2  0  2  2  2  2  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  2  2  0  2  0  2  2  0  0  2  0  2  0  0  0  2  2  0  2  2  0  2  0  2  0  2  2  0  2  0  2  2  2  2  2  2  2  2  2  0  0  2  2  0  0  2  2  0  0  0  2  2  2  0  2  2  2  2  2  0  0  2  0  2  0  0  0  2  2  0  0  0  2  0  0  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+65x^72+44x^74+24x^75+267x^76+208x^77+200x^78+544x^79+450x^80+1192x^81+308x^82+1728x^83+555x^84+2448x^85+432x^86+2448x^87+527x^88+1728x^89+308x^90+1192x^91+355x^92+544x^93+200x^94+208x^95+213x^96+24x^97+44x^98+68x^100+34x^104+16x^108+6x^112+3x^116

The gray image is a code over GF(2) with n=344, k=14 and d=144.
This code was found by Heurico 1.16 in 22.1 seconds.