The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  2  2  0  1  0  0  2  2  1  2  0  0  1  2  1  1  1  2  1  1  1  2  0  1  1  1  2  0  1  0  1  2  2  1  2  1  1  2  1  1  1  1  1  1  0  2  0  1  1  1  0  1  1  1  1  0  0  1  1  1  1  0  1  2  1  1  2  2  2  0  1  1  1  2  1
 0  1  0  0  0  1  1  1  0  0  3  3  1  2  1  3  1  0  2  0  0  1  1  1  0  1  1  1  0  0  2  1  1  2  2  3  1  1  1  1  0  1  0  1  2  1  1  3  0  2  1  2  0  3  2  1  1  2  1  2  2  2  1  3  2  0  3  1  0  1  3  0  2  2  1  0  3  0  1  1  1  2  2  3  1  0  0
 0  0  1  0  1  1  0  1  0  1  1  2  0  1  3  2  1  1  1  0  0  0  3  0  0  1  1  2  1  0  3  3  0  1  2  1  1  1  0  1  3  1  3  2  1  0  3  1  0  1  0  1  1  2  0  1  2  1  2  0  2  3  3  1  0  0  1  2  1  0  1  3  3  1  3  1  0  2  1  3  2  0  3  3  2  0  0
 0  0  0  1  1  0  1  1  1  0  1  2  1  3  0  2  1  3  0  1  1  2  1  1  0  2  3  1  1  1  3  2  1  0  1  3  2  3  3  3  0  0  0  0  3  2  0  1  3  2  2  0  0  1  0  0  0  3  1  2  2  0  1  2  1  2  1  0  2  2  1  3  3  0  0  2  3  0  1  3  3  1  3  0  1  2  0
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  0  2  0  2  0  2  2  2  0  2  2  0  0  0  2  2  2  2  0  0  0  2  0
 0  0  0  0  0  2  0  0  0  0  0  0  2  0  0  2  0  2  0  0  2  2  2  2  2  0  0  2  0  2  2  0  0  0  2  2  2  2  2  0  2  0  0  2  0  2  2  2  2  2  2  2  2  0  0  2  0  2  0  2  2  0  0  0  0  2  2  0  0  0  2  0  0  0  0  2  2  0  0  0  2  0  2  0  0  2  0
 0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  0  2  2  2  2  0  2  2  2  2  0  0  0  0  0  0  2  2  2  2  0  2  0  2  0  2  2  0  2  2  2  2  2  0  0  0  0  2  0  2  2  0  2  0  2  2  2  0  0  2  0
 0  0  0  0  0  0  0  2  0  0  2  2  0  0  2  0  2  2  2  2  0  2  2  2  2  0  0  2  2  2  2  2  0  0  2  0  0  2  0  0  0  0  0  0  0  2  2  0  2  0  0  0  2  0  2  2  2  0  2  2  2  2  2  0  2  0  2  2  0  0  2  2  0  0  2  0  2  0  0  2  0  2  0  0  0  0  0
 0  0  0  0  0  0  0  0  2  0  2  0  0  0  0  0  2  2  0  2  2  2  2  0  2  2  2  0  2  0  0  2  0  0  2  2  2  2  2  2  0  0  2  2  0  2  0  2  0  0  0  2  2  2  0  0  0  2  2  0  2  2  2  2  0  0  2  2  0  2  2  0  2  0  2  0  0  2  2  2  0  2  0  0  0  2  2
 0  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  2  0  0  2  0  2  2  2  0  0  2  0  2  0  0  0  2  0  2  2  0  2  2  2  0  2  2  0  0  0  0  0  0  2  2  0  0  0  0  2  0  2  2  2  2  2  0  0  2  0  0  2  2  2  2  2  0  2  0  2  2  0  0  2  2  2  0  2  0  2  2

generates a code of length 87 over Z4 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+73x^72+82x^73+196x^74+230x^75+342x^76+344x^77+461x^78+544x^79+653x^80+744x^81+681x^82+800x^83+835x^84+884x^85+887x^86+932x^87+861x^88+908x^89+855x^90+876x^91+721x^92+680x^93+587x^94+480x^95+408x^96+368x^97+313x^98+200x^99+159x^100+76x^101+89x^102+28x^103+34x^104+10x^105+17x^106+6x^107+5x^108+8x^110+2x^112+2x^114+2x^116

The gray image is a code over GF(2) with n=174, k=14 and d=72.
This code was found by Heurico 1.16 in 61.1 seconds.